How can I defend and build up early-game in the campaign as Eldar in Dawn of War: Dark Crusade?

Eldar units are fairly fragile to start with, but make up for it with the upgrades available to them and being quite effective in numbers.

As you are talking about early game tactics against an established enemy, you will want to focus on numbers rather than holding out for vehicles and heavier units.

Guardian squads with a Warlock in the unit will increase their damage by 20% and also increase your population cap allowing for more units, helping with what should be your main strategy here.

Your next priority should be upgrades for your guardian/warlock squads. The Warlock can be upgraded with Mysticism at a cost of 150 Req and 75 Pow - This will get them a highly effective close combat weapon, a morale boost to the whole squad and a spell that can immobilise enemies for around 7 seconds.

Dark Reapers are also good early game, again with upgrades making them even more effective. An Exarch in the squad will increase damage by 15%, and fully upgraded optics will increase damage up to 125%.

If you have a Farseer with the Guide spell, it's apparently bugged and can give a squad over 100% accuracy. This coupled with the Dark Reapers ability to move while shooting should be quite effective.

The Optics and Armour upgrades are essential as early as you can get them.

A good resource for stats and tactics on each Eldar squad can be found here.

And some tips against particular armies can be found here.