If there is no video output to an external monitor, changing ribbons won't help, the fault is before it gets that far, as others have said, on the grpahics chip, which is usually built into the motherboard. Testing a laptop motherboard isn't so easy as a desktop one, not least because it is like heart surgery taking it all apart, compared to a 5 minute job removing a desktop one.

This page (not mine!) has a diagnostic http://www.daileyint.com/hmdpc/lcd.htm

If the GPU is kaput you could send it to somebody like this to have them reball it for you: http://cgi.ebay.co.uk/Sony-Playstation-3-PS3-Reball-Service-YLOD-/270711558910?pt=LH_DefaultDomain_3&hash=item3f07aa92fe#ht_3784wt_672

Lead-free solder is the main cause of all these GPU problems!

npm: reballing doesnt cure the issue, merely delays its reonset sadly, sometimes it doesn't even work, problem is a lot of the time that the GPU itself is totally and utterly fried due to the poor heat dissapation due to the bad design of the cooling system.