The CMOS battery is mostly used to keep the settings set where they're supposed to be and keep the time on your clock on the computer set when the power is disrupted to your computer.
But yes sometimes a CMOS battery that is either or dead can cause the computer to not boot at all.
If your computer starts up but never boots up or shuts off soon after starting it then the CMOS battery could be dead and need replaced.
It's worth a try to replace the CMOS battery to see if it fixes the boot up problem with your computer.
I had a computer that wouldn't boot up properly and after changing the CMOS battery the computer booted right up like it should so I would certainly lean towards a bad CMOS battery causing the boot up failure of your computer.
But then again it can be other problems such as loose RAM or a bad stick of RAM that can also cause a computer to fail to boot up.