If possible, before logging into live chess again, can you try clearing your browser cache?
If you're unsure of how to do this, this link provides a step by step guide on how to clear the browser cache.
http://support.chess.com/Troubleshooter/Step/View/2
or this one
http://www.chess.com/clear_cookies.html
This generally clears problems with pieces not moving or pieces disappearing in live chess .
Also, make sure your mouse is clean and free from dirt/dust.
I logged on to live chess after long time... but often I am having problems to move pieces...
often I am not able to select a particular piece ... any idea why...