Send a ticket to support (http://www.chess.com/forum/view/help-support/how-to-send-in-a-support-ticket) rather than naming and shaming (which is against the site policy).
Chess.com live chess rule breaker.
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Hello staff of Chess.com, it's a pleasure for me to be able to play and train on this amazing chess website. I have been a member for over a year now, and today, 6/21/14, I've noticed that a member from the community has been abusing the system. I'd like to tell you about franka9 (Australia) who has been holding a game up after I took his queen. Its a 15 | 5 rated game. He claims he has to go and offers me a draw eleven times so far (Game still going on), which I decline all times. He then reconnects and joins a lot of times and says that he will not resign until I accept his draw, he is not moving at all.
Proof:
http://gyazo.com/cac7b61e80a235b01c5c678610d28116
http://gyazo.com/cfa1045b1428248f82885f00e9a449fb
http://gyazo.com/a34580490362f49e4c396e240a1b1c90
Hopefully you can take action soon if necessary.
Thanks for your time,
Nerfgunwar.