pieces will not stay in new locations and I cannot proceed. what's wrong?

Try rebooting your computer and see if it goes away. 

If you aren't talking about chess.com then it probably means someone has glued your pieces to the board .

Try refreshing the game, and make sure your browser is up to date.  Also try clearing your local cache and refreshing.  If these aren't it, you might be trying to make an illegal move, though, with your rating I'm highly doubting that ;)

Also try Chrome, and check if your java is up to date.

Busted.