It kind of sounds to me like the PSU fan.
My wife's PC had the same basic problem.
It was the PSU fan. If the fan wouldn't start then
the PC wouldn't start.
I would give the the whole PSU a good cleaning and
take the fan out and grease the bearing.
As for the accelerator, I also have an A3000d-16mhz.
I installed an A3640 card and it runs very nicely.
I know there was a hack that cut a trace on the 16 mhz
machines to make then 25 mhz. I don't know just what was
involved. The info is probably available on Aminet if you
are interested.
Mel