You could just sell the new monitor on eBay and buy a nice rosewill monitor off newegg.com for relatively cheap. It all depends on if you want to take the chance that HP is actually going to ship you a quality component this time.
Just spoke with a customer service person at HP Tech support. He confirmed that the black out problem was not due to a power adapter, but rather all earlier makes of HP LCD monitors in general. They had sent me a replacement power adapter. I plugged it in and it worked all of 3 seconds before the monitor blacked out again!
They are sending me a replacement monitor. I am concerned that this monitor may begin blacking out after my warranty expires. The warranty continues on from the original purchase date, not the date of the replacement. He asked if I wanted to buy an extended warranty, but I refused. I told him I shouldn't have to buy something else to get what I paid for to begin with.
He was very helpful and cordial (and actually was an American who spoke good English to boot).