Try disabling your sound card and then play OFP and see if it crashes. You can disable the card by opening Sytem Properties then the Device Manger Tab, then open "Sound Video and game controllers". Now select your sound card and press the "Properties" button. Then check "Disable in this hardware profile" and the hit the "OK" button. Your sound card icon should now have a little red X through it.
If the Game is now OK you know the sound card/driver/directX is most likely the problem.
Playing OFP without sound is almost impossible but at least it might help solve the problem.
A lot of people appear to be having sound problems recently and not just with OFP. I have tried Avon's solutions but they have not helped.
New System:
MB: A7V266-E
BIOS: 1004B
CPU: Athlon 1900+
HDD: 40GB (35GB Free)
RAM: 512 MB DDR2100
Video Card: Hercules Geforce3 Ti200
MS Windows: Win98SE
MS Explorer: 6
MS DirectX: 8.1