That doesn't sound good. If you don't have your own tester tool, take the power supply to an Autozone or Radio Shack, any store that's going to have a multimeter handy.
Here are the Pro HD's PS specs (Solo, SlingCatcher and Pro HD all use the same adapter):
If the power supply is kaput, that's one thing- you can replace it for $20 or less. If it's working, you might have a failed Slingbox.
Either way, your description sounds like a definite hardware failure. Primary Clue: You should have some sort of LED light activity on power up.
Wish I had a more optimistic assessment. Good luck !