I assume you've unplugged from the mains, waited a few mins and restarted and also that you've done the Factory Restore from the same menu as Restart and Diagnostics.
Unfortunately if you've done those steps you are likely to be stuck.
There is no other official way to restore the shipping AppleTV backup image.
Apple are unlikely to be able to offer assistance if out of warranty though you could try, and even then I have no idea if they'd offer a repair/replacement as the unit is no longer sold.
There might be unofficial ways you could try and kick the thing into action if you Google for AppleTV jacks etc, but you might make trhings worse than they are (difficult to make igt more non-functional than it is).
Your best bet if Apple are unable to help would be to try and source a second hand unit (or maybe old stock). If a second hand unit had a working hard drive of similar capacity you might be able to clone that onto your existing one but that would generally entail opening the units up. No guarantee that thsi would help if some other component was stopping AppleTV from working.
Final though, if anything has changed eg HDMI cable/TV etc then try another or try component out in case HDMI negotiation is somehow tripping it up.
Good luck.
AC