Sounds like its going into auto protect shutdown. Try holding the imputand menu bottons in together for 5 seconds and see if the green light blinks out a series of blinks. If so notice what they are, should be a 2 digit code if its going into shut down. If not its a power supply issue. Also you can look the boards over for evidence of CRT fluid leaking on the boards, I have seen this happen alot to the VS models it causes corrosion of the components and you will experience no start up condition like the one your describing.
Usually answered in minutes!