On my desktop A3000 I have noticed that sometimes SCSI termination problems result in the Amiga turning on, but only giving a black screen (i.e. acting dead). Try plugging / unplugging devices from the external SCSI port on the back (not while the machine is on). Try using an ACTIVE DB-25 SCSI terminator on that external port. Try terminating your internal SCSI devices, or remove all SCSI devices entirely. Lastly, disable the onboard SCSI and see if you can get it to turn on (is there a jumper to do this?).
Please post your results to let us know how it works out for you.