Interesting. If you're getting nothing but black, no error messages, no access to setup, nothing - then it does sound like an issue with either the firmware (BIOS) or hardware. Another possibility is the computer is hung in a suspended state.
Some PCs have a provision to reflash a tatered bios using a key sequence or by booting from a specially prepared USB drive (usually a thumb drive). You might look for info on your PC maker's support site, or you might have to search some user forums for the info.
But first you should try this if you haven't yet - Start the computer, make sure it is running (indicator light, fan, etc. are on), then push the power button and hold it in, probably at least ten seconds, until you hear the whole system click off. Then turn it on again and see if you get a more normal looking startup sequence.
But it does seem that the first thing to do is see if the old box can still get things going prior to kicking the operating system into gear....
Mark to recheck.
The Jag is running down like a cheap clock spring.