If it has been stored for a long time and suddenly under a lot of use my guess would be that over time the elctrolyte in the capacitors has broken down and in using it they've destroyed them selves.
Assuming you've tried all the basic steps:
Tried another PSU
Tested all Video outputs
Made sure Roms are seated correctly (For this I'd remove the FastATA and fit Roms directly)
You should get the Purple Rom screen even without any keyboard/mouse/floppy connected but there may be a delay of up to 30 seconds. If you're not even getting this far the I'd look to have the Capacitors replaced.
All the best,
Steve.
