The machines have a HD? If so, it could be only the re-validation process acting up.
To keep it simple: turn the machine on and wait for a couple of hours.
Usually when you have a validation problem, the machine don't boot. It lits both leds (hard drive and power) for time needed to re-validate the system.
Bad socketed ROM could be an issue, too. Open the Amiga and press gently, but tight, the ROMs into the socket.
