The battery on the motherboard keeps all your BIOS settings and real time clock going etc, wouldn't hurt to replace it if it is the watch type should be fairly easy. I wouldn't expect that to be cusing your PC to be locking up, it sounds like you are multi tasking and could be getting low on resources. It may be worth putting the resource meter on your desktop to see if this is happening, although this uses resources in itself. The other thing to do is make sure you have the latest graphics drivers installed, latest BIOS update etc etc.
I presume you are talking desktop and not laptop? Make sure all power saving is off in the BIOS and Windows, this causes no end of problems, more trouble than it's worth. It could bew that you are not using your HDD and it is powering down and causing the lock up, so make sure ALL power saving functions are off. Regularly defrag HDD. Is Windows managing your swop file, is there sufficient space on the drive/partition for the swop drive. Check for any conflicts in device manager.