Your computer's BIOS chip is a CMOS (Complementary Metal–Oxide–Semiconductor) chip that stores a set of very low-level drivers. These drivers regulate the interaction of the CPU with the various other components of your motherboard. Like any computer hardware component, BIOS (Basic Input Output System) chips can fail due to overheating, over voltage, or even the random interactions of cosmic rays making it down through the atmosphere. BIOS chips can be rewritten (or flashed) with updated drivers. And they can usually be reset to a factory default state by removing the battery that's linked to them on the motherboard.
First Symptom: System Clock Resets
Your computer uses the BIOS chip to maintain its record of the date and time. This can be updated by the operating system. But deep down at the hardware level, this is a BIOS function. If your system always shows a date or a time that's several years out of date when booting up, you've got one of two things happening: Your BIOS chip has been damaged, or the battery on the motherboard has died. The batteries have expected lifespans of a decade or so. The likely cause is a battery that needs replacing. These are standard 'coin format' batteries. If replacing the battery doesn't fix the problem, it's a bad BIOS chip.
Second Symptom: Inexplicable POST Problems
When your computer is powered on, the Power On Self Test (or POST) checks the low-level hardware status of hard drive controllers, RAM and the interconnections (the front side bus between them). If all goes well, when you power up the computer, there's a set of 4, 5 or 6 faint clicks, depending on the BIOS. When the POST problem encounters problems there are a series of short beeps. When a computer that has been working reliably suddenly develops POST problems without having had its BIOS updated, this is a good indicator that the BIOS chip may be failing.
Third Symptom: Failure to Reach POST
If your computer spins up the fans on the power supply or the case fan when powered on -- but doesn't give a POST message on the screen, or give an option to hit a function key to reach the BIOS setup -- this is another indicator that there may be a problem with the BIOS.