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!