Try to run the system on a Knoppix or Ubuntu Live CD. This will give you an idea about the system's health, as you can go web browsing, try out word processing etc. No installation is required. If neither of these environments will run OK, you could very well have a hardware problem; if they DO run nicely, you should suspect your windows installation and a format + reinstall is what I'd recommend.
Updating the BIOS seems a bit scary on a flaky system and I advice against that. BIOSs don't go bad by themselves; if the system has worked and now doesn't, it's not the BIOS, it's the O/S, drivers, malware or hardware.
/RID