Okay, so there are some possibilities about this problem:
1) You need to download Google Chrome.
2) This may be a problem that Chess.com is working on now.
3) This just may be a bug.
This has been happening to other people because there is another post in the Help and Support forums with the same question and he says it freezes around the 36th move, too. What I would suggest is downloading Google Chrome first, maybe update your Java, and if that doesn't work, then Contact the Chess.com Help and Support through this link:
http://support.chess.com/Tickets/Submit
Alot of the times, some problems are caused by having Internet Explorer, instead of better versions of Internet, such as Google Chrome. But I think the Chess against the computer uses Java, unless you are playing Chess against the computer on Live Chess. There has been many problems with playing against the computer, so if you download Google Chrome and update your Java, then it should work. If it doesn't then Contact the Chess.com Help and Support through the link I provided. I hope this will help!
-BlueGator456
Is there a problem with Chess.com when playing the computer?
I've run into the following problem on different computers.
When playing the computer, on Black move #36, the message under the chess board says computer thinking... But it stays this way until I close the browser. I've tried this on different computers with the same result. Is this currently a problem?
Thank You