Welcome, Newcomer. If your CMOS battery is failing, it could be reseting any changes made to your BIOS. A good way to test this is to "load optimized defaults" in your BIOS. If the boot order changes back to HDD being third, this may be the cause. With HDD as priortiy 3, your boot order would probably be 1. Floppy, 2. CD/DVD, 3. HDD, 4. USB or other external device.
A failing PSU can explain why a hard drive doesn't power up, and subsequently doesn't boot, but I can't think of any reason why a failing PSU would change your BIOS settings.