OK, this is actually a bunch of different questions, because you don't seem to actually know what you're asking.
First, you don't generally need to mess with the BIOS at all to reinstall the OS (except maybe to set the boot order for your drives so you can boot off a DVD or flash drive). If you can boot from it, you just pop in your CD/DVD or flash drive, and reboot. Then the OS installer will come up and you follow the instructions on screen.
Second, messing with the BIOS settings or anything to do with the BIOS or CMOS won't do anything about the Operating System password. That's stored on your hard drive and has nothing to do with the BIOS settings. So, popping the CMOS battery won't do anything even if your board was old enough that it reset the BIOS password, that's a totally different thing from the one your operating system asks for. On anything made after 1988, popping the CMOS battery won't do anything to the BIOS password because it's stored in non-volatile flash RAM. I'm not exactly sure why that is, because it's still pretty easy to defeat on a desktop computer.
If you wanted to reset the BIOS password -- again this is NOT the OS password: On modern motherboards and laptops, popping out the CMOS battery does NOT reset the BIOS password. You can reset the BIOS password using a jumper on the board. You find the jumper location in the motherboard manual, short it with a jumper patch and turn on the system. It'll reset all Motherboard settings back to factory defaults including the BIOS password (default is usually blank). Then you have to remember to shut down and pull that jumper, or it'll keep reseting everything on every boot up.
On a laptop, this generally isn't an option, because it makes it too easy to get a stolen laptop back into action. If this is a laptop, you'll need to contact the manufacturer for a master BIOS password, and you'll have to prove you're the legitimate owner or they won't give it to you.
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Finally to the question you put in the title (which has nothing to do with the stuff you're asking in the body text):
No, an almost dead CMOS battery will NOT prevent you from entering the BIOS settings menu. Provided you're pressing the right key(s) at boot to get into the BIOS settings (check the motherboard manual, as it really varies by manufacturer), you'll get in there. The only thing that will happen if you have a dead or near dead CMOS battery is that your settings won't save. Each time you boot up, it'll always use the factory default settings until you pop in a new CMOS battery -- except the BIOS password if you set one (see above for details).