496MB(????) of RAM - and 16mb given over to video total 512mb RAM - so that's fine
"system disk is 10GB, and has 461 MB free space, and the data disk is 17.7 GB with 6.64 GB free space (so I'm assuming that the problem isn't virtual memory)."
It depends on where the virtual memory is - right click my computer and choose
and point virtual memory to the bigger partition.
I think it's the "10GB, and has 461 MB free space" causing problems.
Can you go back via system restore to before the udpate?
It seems to me that the laptop should run ok - not wonderfully, but ok. Is it a celeron processor?