If plugging the monitor into a different electrical outlet doesn't help (and I doubt it will help), and checking the power cord shows nothing wrong: do you know how long the warranty is on the monitor?
Sounds like the fluorescent tube inside the montior is on the fritz. If the monitor is under warranty, HP should fix it for free.
If not, then fixing the monitor will likely cost more than buying a new one. You can probably get a 19" LCD monitor very cheap. As for what brand, as long as you stick with a brand name they're generally all okay. Some no-names are iffy.