Assign the IRQ's manually in the bios if it will let you.
Try loosening the memory timings again if it will let you.
Its also possible its the Ali IGP causing it, try a different PCI VGA card
Memtest86+ has a floppy image, it has problems with some floppy drives, and will endlessly try to boot, but works on most.
http://www.memtest.org/#downiso

I just realized how are you gonna get the floppy iso or raw exe to your machine, if you have no CD-R\Floppies?
Does the machine have a nic of some type?? I suggest tracking some Floppy disks down from a local thrift store!

What board? any pics?
No bad caps? or bad Tag cache ram.
Try cleaning the memory connection pins.

It could be hardware or software. What operating system are you using? If you have Windows, run the DOG games from MS-DOS mode.

I had a problem with a socket 7 pc having similiar issues. Playing games for a while would make the game lock up or crash. The IDE cables in the computer were dirty (the computer was sitting in some shed and was given to me) and looked really cheap. I replaced the cables and the problem went away. Reapplying thermal on the CPU won't hurt either. When I checked mine it was almost non-existant and the heatsink was extremely hot to touch.