Could be it can't find the OS. Perform a PRAM reset. Turn off computer. Locate the "command," "option," "P" and "R" keys on your keyboard. Press power button to turn Mac Mini on. Immediately press down on the command, option, P and R keys simultaneously and hold them down. Try to do this before the gray screen comes on. Keep holding the four keys until after you hear the start up chime twice, then you can let go. Your Mac Mini should start up fine. This should reset the P RAM. I have had a Mac Mini completely come back to life after doing this. Hopefully, this works for your Mac Mini. Always back up your data. Good luck!