A few things to try.
- Try reseating the ROMs and ROM switcher.
- Check all the solder points on the caps and PCMCIA to make sure there are no shorts and everything is secure.
- Try using a set of ROMs without the switcher
- Make a close inspection of the board and chips to make sure nothing got jarred loose during shipping.
- Check to see if there are any popped resistors or caps. In case there was a short during initial power on.
- See (or more appropriately, listen) to see if you can determine where the buzzing is coming from.
- Get a set of diag ROMs to see if that will report where the issue is.
- If you have a logic probe or oscilloscope, you can check to see if the CPU is getting timing signals.
- If you have a multimeter you can check Vcc points to see if there are voltages where there needs to be.