Will Lego repair a bad motor? I have the Electric Technic Micromotor:

http://www.peeron.com/inv/sets/5119-1

and it simply won't come on. I seem to recall at some point someone telling me a long time ago, that if you sent parts to Lego, they'd repair them. Do they have a warranty or lifetime guarantee? How would I go about getting it repaired?

I also have several of the Electric Technic Mini-Motor 9v, probably about 8-10, and three of them aren't working. Anyone have any success fixing those?
The LEGO customer service does provide replacements for defective parts, but only for parts which are still in production. Sometimes you'll need to send the broken part back to them. They don't repair the parts as such, just replace them.

As for the micromotor, you're out of luck as it's not produced anymore. They might provide another motor as a replacement, but that's not going to help you much.

Your next option is to buy a second-hand one, for example on Bricklink (service pack or motor alone)