Rear Derailleur won't move
I saw a bike with a similar problem last weekend, but as other people have said, it's hard to know the correct answer without pictures and a better description. 

In his case, the derailleur cage had somehow sprung past the stopper and the spring was fully unwound. The result was that the derailleur did not provide any chain tension. 

Fixing it required:


Remove the chain
Rotate the cage against the spring and past the stopper, which was hard to get past
Put the chain back on. 


After that it worked perfectly.