Can you restart a quest from the beginning?

I'm currently doing the quest "Diplomatic Immunity" and I'm stuck. I wish to begin the quest over again so I can continue on with the game.

If you're playing on PC and don't want to/cannot simply reload an old save (Which is always the safest option) you can use this console command to reset that quest.

resetquest <questid>

Open the console by pressing the tilde key (usually found directly under the escape button), enter that command with the relevant quest ID, and it will reset that quest.

The only way I know of to find out the quest's ID was to use this thread

Thread contents included for future proofing (ID is the part in brackets after quest name):

//\\Main Quest - Act I:

Unbound (mq101)
Before the Storm (mq102)
Bleak Falls Barrow (mq103)
Dragon Rising (mq104)
The Way of the Voice (mq105)
The Horn of Jurgen Windcaller (mq105ustengrav)
A Blade in the Dark (mq106)

//\\Main Quest - Act II:

Diplomatic Immunity (mq201)
A Cornered Rat (mq202)
Alduin's Wall (mq203)
The Throat of the World (mq204)
Elder Knowledge (mq205)
Alduin's Bane (mq206)

//\\Main Quest - Act III:

The Fallen (mq301)
Season Unending (mq302)
Paarthurnax (mqpaarthurnax)
Season Unending (mq302)
The World-Eater's Eyrie (mq303)
Sovngarde (mq304)
Dragonslayer (mq305)

//\\The Companions Quests (Faction):

Take Up Arms (c00)
Proving Honor (c01)
The Silver Hand (c03)
Blood's Honor (c04)
Purity of Revenge (c05)
Glory of the Dead (c06)

//\\The Companions - Radiant Quests:

Initial Wave: Animal Extermination (I) (cr01)
Initial Wave: Animal Extermination (II) (cr02)
Initial Wave: Hired Muscle (cr04)
Initial Wave: Trouble in Skyrim (cr05)
Initial Wave: Family Heirloom (cr06)
Initial Wave: Escaped Criminal (cr07)
Initial Wave: Rescue Mission (cr08)
Second Wave: Striking the Heart (cr09)
Second Wave: Stealing Plans (cr10)
Second Wave: Retrieval (cr11)
Final Wave: Totems of Hircine (cr12)
Final Wave: Purity (cr13)
Final WAve: Dragon Seekers (cr14)

//\\The College of Winterhold Quests:

First Lessons (mg01)
Under Saarthal (mg02)
Hitting the Books (mg03)
Good Intentions (mg04)
Revealing the Unseen (mg06)
Containment (mg05)
The Staff of Magnus (mg07)
The Eye of Magnus (mg08)

//\\The College of Winterhold - Radiant Quests

Rejoining the College (mgrejoinquest)
Tolfdir's Alembic (mgr01)
Out of Balance (mgr02)
Enchanting Pick-Up (mgr10)
Restocking Soul Gems (mgr11)
Fetch a book for Urag Gro-Shub (mgr20, mgr20b)
Shalidor's Insights (mgr21)
The Atronach Forge
Forgotten Names
Aftershock (mgr30)
Rogue Wizard (mgrrogue)
Arniel's Endeavors (mgrarniel01 - mgrarniel04)
Filling Soul Gems (mgr12)

//\\The College of Winterhold - Apprentice Radiant Quests:

Brelyna's Practice (mgrappbrelyna01)
J'Zargo's Experiment (mgrappjzargo01)
Onmund's Request (mgrapponmund01)

//\\The College of Winterhold - Ritual Spell Radiant Quests:

Destruction Ritual Spell (mgritual01)
Illusion Ritual Spell (mgritual02)
Conjuration Ritual Spell (mgritual03)
Restoration Ritual Spell (mgritual04)
Alteration Ritual Spell (mgritual05)

//\\Thieves Guild Quests:

A Chance Arrangement (tg00)
Taking Care of Business (tg01)
Loud and Clear (tg02)
Dampened Spirits (tg03)
Scoundrel's Folly (tg04)
Speaking with Silence (tg05)
Hard Answers (tg06)
The Pursuit (tg07)
Trinity Restored (tg08a)
Blindsighted (tg08b)
Darkness Returns (tg09)

//\\Thieves Guild - Radiant Quests:

No Stone Unturned (tgcrown)
Reparations (tgban)
Shadowmarks
Moon Sugar Rush (tgfencecaravan)
Armor Exchange
The Litany of Larceny (tglarceny)

//\\Thieves Guild - City Influence Quests:

Silver Lining (tgtq01)
The Dainty Sload (tgtq02)
Imitation Amnesty (tgtq03)
Summerset Shadows (tgtq04)

//\\Thieves Guild - Leadership Quest:

Under New Management (tgleadership)

//\\Thieves Guild - Extra Quests:

The Bedlam Job (tgrnt)
The Fishing Job (tgrgf)
The Numbers Job (tgrfo)
The Burglary Job (tgrbe)
The Shill Job (tgrdu)
The Sweep Job (tgrhc)
The Heist Job (tgrsl)

//\\The Dark Brotherhood Quests:

Delayed Burial (db01misc)
Innocence Lost (db01)
With Friends Like These... (db02)
Sanctuary (db02a)
Sentenced to Death (db03)
Whispers in the Dark (db04)
The Silence has been Broken (db04a)
Bound Until Death (db05)
Breaching Security (db06)
The Cure for Madness (db07)
Recipe for Disaster (db08)
To Kill and Empire (db09)
Death Incarnate (db10)
Hail Sithis! (db11)

//\\Dark Brotherhood - Side Contracts:

Part 1 - Kill Narfi (dbsidecontract01)
Part 2 - Kill Beitild (dbsidecontract03)
Part 3 - Kill Ennodius Papius (dbsidecontract02)
Part 4 - Kill Hern (dbsidecontract04)
Part 5 - Kill Lurbuk (dbsidecontract05)
Part 6 - Kill Deekus (dbsidecontract06)
Part 7 - Kill Ma'randru-jo (dbsidecontract07)
Part 8 - Kill Anoriath (dbsidecontract08)
Part 9 - Kill Agnis (dbsidecontract09)
Part 10 - Kill Maluril (dbsidecontract10)
Part 11 - Kill Helvard (dbsidecontract11)
Part 12 - Kill Safia (dbsidecontract12)
Destroy the Dark Brotherhood! (dbdestroy)
Where You Hang Your Enemy's Head (darkbrotherhoodsanctuaryrepair)

//\\Dark Brotherhood - Radiant Quests:

Honor Thy Family (dbeviction)
The Feeble Fortune
Welcome to the Brotherhood
Cicero's Return
The Dark Brotherhood Forever! (dbrecurring)

//\\Civil War Quests - Imperial Legion:

Joining the Legion (cw01a)
The Jagged Crown (cw02a)
Message to Whiterun (cw03)
Defense of Whiterun
Reunification of Skyrim - A False Front (cwmission03)
Reunification of Skyrim - The Battle for Fort Dunstad (cwfortsiegefort)
Reunification of Skyrim - Compelling Tribute (cwmission07)
Reunification of Skyrim - The Battle for Fort Greenwall (cwfortsiegefort)
Reunification of Skyrim - Rescue from Fort Kastav (cwmission04)
Reunification of Skyrim - The Battle for Fort Amol (cwfortsiegefort)
Reunification of Skyrim - Battle for Windhelm (cwsiegeobj)

//\\Civil War Quests - Stormcloaks:

Joining the Stormcloaks (cw01b)
The Jagged Crown (cw02b)
Message to Whiterun (cw03)
Battle for Whiterun (cwsiegeobj)
Liberation of Skyrim - Rescue From Fort Neugrad (cwmission04)
Liberation of Skyrim - Compelling Tribute (cwmission07)
Liberation of Skyrim - The Battle for Fort Sungard (cwfortsiegefort)
Liberation of Skyrim - A False Front (cwmission03)
Liberation of Skyrim - The Battle for Fort Snowhawk (cwfortsiegefort)
Liberation of Skyrim - The Battle for Fort Hraggstad (cwfortsiegefort)
Liberation of Skyrim - Battle for Solitude (cwsiegeobj)

//\\Daedric Quests:

The Black Star (da01)
Boethiah's Calling (da02)
A Daedra's Best Friend (da03)
Discerning the Transmundane (da04)
I'll Met by Moonlight (da05)
The Cursed Tribe (da06)
Pieces of the Past (da07)
The Whispering Door (da08)
The Break of Dawn (da09)
The House of Horrors (da10)
The Taste of Death (da11)
Darkness Returns (tg09) (Part of the Thieves Guild Quests)
The Only Cure (da13)
A Night to Remember (da14)
The Mind of Madness (da15)
Waking Nightmare (da16)

//\\The Greybeards Quests:

Word Wall Revelations (wicastmagic04)
Meditations on Words of Power

//\\The Blades Quests:

Rebuilding the Blades
Dragonslayer's Blessing
Dragon Research
Dragon Hunting

//\\The Bards College Quests:

Tending the Flames (ms05)
Finn's Lute (bardscollegelute)
Pantea's Flute (bardscollegeflute)
Rjorn's Drum (bardscollegedrum)

//\\Temple Quests:

The Heart of Dibella (t01)
The Book of Love (t02)
The Blessings of Nature (t03)

//Side Quests:

Blood on the Ice (ms11, ms11b, ms11kicker, ms11essentializing, ms11wuunfertharrest)
Forbidden Legend (dungauldursonqst)
The Forsworn Conspiracy (ms01)
No One Escapes Cidhna Mine (ms02)
The Golden Claw (ms13)
In My Time of Need (ms08)
Kyne's Sacred Trials (dunhunterqst)
Laid to Rest (ms14)
Lights Out! (ms07)
The Man Who Cried Wolf (ms06start)
The Wolf Queen Awakened (ms06)
Missing in Action (ms09)
Promises to Keep (ms03)
A Return to Your Roots (nn01)
Rise in the East (ms10)
Rising at Dawn (vc01)
Unfathomable Depths (ms04)
The White Phial (ms12)
Repairing the Phial (ms12b)
Captured Critters
The Forgemaster's Fingers (favororcsintro)
The Great Skyrim Treasure Hunt
Masks of the Dragon Priests

//\\Dungeon Quests and Other Activities:

Angarvunde: Medresi Dran and the Wandering Road (dunangarvundeqst)
Ansilvund: A Love Beyond Death (dunansilvundqst)
Angi's Camp: Composure, Speed, and Precision
Bard's Leap Summit: Leap Before You Look
Blind Cliff Cave: Melka and Petra The Affairs of Hagravens (dunblindcliffqst)
Darklight Tower: Repentance (dundarklightqst)
Forelhost: Siege on the Dragon Cult (dunforelhostqst)
Frostflow Lighthouse: What Lies Beneath (dunfrostflowabyssqst)
Frostmere Crypt: The Pale Lady (dunfrostmerecryptqst)
High Gate Ruins: A Scroll for Anska (dunhighgateruinsqst)
Hillgrund's Tomb: Ancestral Worship (dunhilgrundstombqst)
Mistwatch: Forgetting About Fjola (dunmistwatchqst)
Moss Mother Cavern: Hunter and Hunted (dunmossmotherqst)
Nchland-Zel: The Lost Expedition
Nilheim: The Nilheim Scam - Telrav's Request (dunnilheimqst)
Ragnvald: Otar's Mad Guardians (dunragnvaldqst)
Rebel's Cairn: The Legend of Red Eagle (dunrebelscairnqst)
Robber's Gorge: Robber's Gorge (dunrobbersgorgeqst)
Shipwreck: Trius' Trinket (dunshipwreck04qst)
Shroud Hearth Barrow: Wilhelm's Specter - Lifting the Shroud (freeformivarstead01)
Shroud Hearth Barrow Location Code = shroudhearthbarrow01 (and 02)
Sleeping Tree Camp: The Secret at the Sleeping Tree (dunsleepingtreecampqst)
Southfringe Sanctum: The Savior of Selveni Nethri
Treva's Watch: Infiltration (duntrevaswatchqst)
Valthume: Evil in Waiting (dunvalthumeqst)
Volunruud: Silenced Tongues (dunvolunruudqst)
YngolBarrow: Ashore in a Sea of Ghosts (dunyngolbarrowqst)

I don't believe this is possible on consoles without major editing to your game.

On a side note, if you are stuck in a location (and fast travel is not an option for whatever reason), you can use a combination of this command and a teleport command to effective restart the quest. Teleport commands are detailed in this question: What is the proper teleport command in Skyrim?

The safest way to do this is simply to reload a previous save. Any thing you do to reset a quest without loading a save, might have undesirable consequences later.