I had this same problem recently (more on that at MD shutting down/not starting up). I’ve since opened up the box and checked the connections, which proved fruitless, so I sent it in to the LA repair center where it’s current being worked on.
One important thing to know is that before sending it I tried one last time to get it up and running so I could save my battery-backed memory to the +Drive. After a few tries, it booted up and immediately went into Factory Reset mode even though I did NOT select it (it wasn’t even on the test/reset screen), which wiped the entire battery-backed memory clean. Fortunately, I didn’t lose much but my strong suggestion, if you’re not already doing it, is to get used to saving to the +Drive early and often.
Good luck and please let us know how it works out.