I have had these symptoms with an 840av: booting occasionally and seemingly working fine when it worked, but mostly not getting past initial powering on, with no chime and no video. That must have started with my 840av about 6 years ago.

At the time, by a stroke of luck I was able to replace the logic board in my 840av with another that I acquired as new service part, believe it or not, from a local ex-dealer, as part of a lot of parts. It worked for 4-5 years, but I then started to get the same symptoms that I had with the older board.

I finally got around to taking a closer look late last year and discovered capacitor failure on both logic boards. In one case, the goo had actually gotten in around the main power connector lines.

A cycle in the dishwasher solved that little problem for a while. Eventually, of course, I'll need to replace the defective parts.

Your trouble may have been drive jumpers, but mine were definitely more deep-seated. I have also just had a Q650 fail, and suspect the caps once again. I guess the time has come to start fussing over capacitors in Quadras in the way we have already learned to do in connection with SE/30s.