Hi,
> Just turning on the A4000. Only a blank grey screen
Just have a look at the "Amiga Guru Book":
green - error in the lowest 256 kilobytes of Chip memory. This might also be caused by a defective CIA-A (memory overlay bit, for example) or Agnus chip.
Reading from your previous floppy problems, I would replace the CIA-chips, or try to swap both, and have a look if the system is running now, but with a bad parallel or serial port.
Noster
EDIT: Sorry, wasn't able to distingish between grey and green :-D
But nevertheless, I would test the CIA's.