You mention what the screen is doing but not the computer - presumably when you say the screen is on standby the computer has switched itself off and is not sending any signals to paint the screen.
I suspect the power supply - it begins to work (do the fans in the machine start to run?) detects bad power and switches itself off. Starts to run etc etc and then gives up.
If it is the power supply it's an easy fix - Four screws and a couple of power connectors. New PSU about £40 - £50 - I bought a second hand one last week for £20 to fix a similar problem.
Good luck...
Peccavi
June 2009