3 (at least) power capacitors
(I used Radio Shack part #272-1032. Any capacitor with the rating of 1000uf @ 10v or better should do though.)
A phillips head screw driver.
A soldiering iron
I take no responsibility if this does not fix your screen! I did this to two of them that would no power on at all before and now they work flawlessly. This is a common problem with these monitors since HP used such cheap parts. Good luck!
Step 1: Remove Stand Cover.
Step 2: Remove Front Cover.
Step 3: Remove Screen From Rear Housing.
Step 4: Time to Reveal the Good Stuff!
Remove the two screws and gently pull out the cable from the bottom of the video and sound board (smaller cover on the left). There should be some "metal" tape along the bottom, just peel it off of the cover, leaving it attached to the frame so you can reattach it later. Putting this shielding tape back in place when reassembling, helps insure noise doesn't interfere anywhere.
Thanks for the heads up Donald Scott!
Step 5: Remove Power Cable.
Step 6: Remove Power Supply Cover.
This is the part where I should say that power supplies can be dangerous and all of that. Just don't be stupid and go poking at things with metal objects and you should be good.
Step 7: Remove the Power Supply.
Lay the screen down again and remove the 4 screws that attach it to the housing. Pay special attention to the top left corner screw. This one is bigger and connects the ground to the metal chassis. VERY IMPORTANT!
Step 8: The Problem Children.
Replace these with the capacitors I talked about in the intro from "the Shack" (it's all I have here sorry... I know they are id10ts) or ones that you picked up somewhere else. Make sure you pay attention to the stripe (the negative side). Installing them backwards will cause them to pop and you will have to do this all over again, if your lucky.
Once you have soldered these three (and possibly others), reassemble! Snap everything back together, screw it all down, etc.
Now plug it in and see if it comes on. It should...
Step 9: DONE!
Let me know if this this works/doesn't work for ya.