You might want to check if it's just a bad power connection first, because a new adapter isn't cheap. They cost about 60 bucks plus shipping from the HP parts department:
Before you shell out that kind of dough, I recommend you first eliminate the obvious like a bad surge suppressor or power strip. Sometimes, one of the outlets in a multi-outlet power strip can go bad and cause just one of the devices plugged in to lose power. It actually happened to me once with a brand spanking new surge suppressor I purchased and I had to go back to the store and get it replaced under the warranty. So, be sure to check by plugging your printer into a different outlet.
If nothing's wrong with your power strip and AC power cord, the next thing to check is the power connector that plugs into the back of your printer. It has three contacts on it, which means there are three points of failure. Unplug it and plug it back in. Wiggle the connector a little, mumble "I hate this stupid printer", and then observe the printer's power light.
Still nothing? Well, if you're feeling a little adventurous and have a basic understanding of how electronic circuits work, you can check the AC adapter to see if it's really dead. You do this by testing the DC outputs of the adapter with a multimeter. Don't have a multimeter? You can either borrow one from a geek friend, or buy your own for about twenty bucks at Radio Shack (get a cheapie model - nothing fancy). IMHO, everyone should own a multimeter. They come in handy for checking batteries and bad connections in low voltage wiring. After you learn to use one, you'll wonder how you ever got along without it.
Anyway, getting back to the printer, the AC adapter has a dual DC voltage output with three pins. The center pin is ground and the two on either side are positive voltages (+36 volts and +16 volts). If the AC adapter is good, your multimeter will indicate at or slightly less than these voltages when tested, around +35v and +15v. A good voltage reading tells you that the AC adapter is probably okay. In that case, the problem is inside the printer itself and buying a new adapter would be a waste of money. At this point, it's pretty safe to conclude that the old mule has finally kicked the bucket.
Hope this helps.