Hi, Ok, sounds like the HDD is working. The BIOS batteries are 3V when new and should be good for 4 to 5 years. You can check them on a multi-meter tester set on DC volts, or a battery tester on the 3V range. The second one is better as it puts the battery under a load, where the voltage will fall to a more realistic level, as in use.
A low battery won't stop the pc from working, but will mean BIOS adjustments by you won't be saved.
A low battery voltage would be about 2.0 Volts (roughly). But even without a tester you would know as the changes you make in BIOS then save, will go back to default, every time you reboot, or next time you switch the pc on.
If you have RAM module faults, it won't get beyond the first 'on screen' POST, so the Linux O/S won't be loaded.
Linux will run on a very low spec pc, if you can find a good 256MB it should boot & run, I would have thought. I have used 512MB.
I have a spare pc running Linux Mint 14, and Ubuntu 12.04, both run well.