A corrupted dataset should cause MySQL to throw an error, not crash.
Corrupted tables are quite easy to check by reading the MySQL manual about the isamchk function. That function will check your data for errors without dumping them out.
I wouldn't try backup up the data now, because now it is already corrupted.
If you would build a copy of the server, you'd build it off a backup that was done before the error started happening.
Note: save your existing backups for now, don't overwrite them. The cause of the problem may have been around for a while, you may have to restore an 'older' backup that you are about to overwrite with the new and corrupted data.
I don't think this is a hardware error (except for HD failure), becuase that would affect the whole system, not just MySQL after some activity.
I guess MySQL barfs out on a bad query (maybe one that either reads corrupted data or one that exceeds the limits of your setup) and doen't release the port.
That way a new MySQL process can't bind to the port.
Check the FAQ's and search search search the net. There's far more info out there than in here :-)