I can't break blocks in Minecraft?

I know the basics: left click is attack, right click is use. I do not have my game on adventure mode, it is on peaceful survival. I do not have cheats on either.

When I put my cursor on something, it doesn't even "highlight" the block like it normally does. If I hold down the left mouse button, it hits once and then stops moving. There are no mining animations nor breaking down of blocks. Essentially nothing happens.

I've checked my settings a million times, and I have restarted the game at least twice. Is there anything I can do to fix it?

Sometimes, especially on multiplayer servers, blocks in the spawn region can't be modified (presumably this is to prevent griefing). If you move about ~100 blocks away, the blocks will behave as expected.