Hi
there are a few things you can try to get stability, even if a bios update is unavailable.
I had this issue with a customer who had invested heavily in an Asus board only 18months before windows 7 came out
He bought windows 7 not checking the compatibility list, thinking obviously anything capable of running Vista should be fine with 7.
Not so, in his case it was the onboard Audio that was causing crashes and BSOD, so I supplied him with a cheap addin Audio card and his system was fine.
Some people report that windows 7 is more fussy about memory controllers, so older processors might also be a problem.
Try disabling features, starting with power management, then in other tests try disabling onboard audio, lan and if possible video.
you can always get a cheap add in card for any of those three.
As a final note before you go spending money, being about 5 years old, the pc could be reaching its end of life, mechanical parts like the HDD, CD-DVD and Fans could start to fail , and you could end up spending a fair amount of money trying to repair the machine, than just buying new components.
Good luck