HP G60 Laptop Screen Goes Blank

I have a three year old HP laptop running Windows 7 (64 bit) that is misbehaving. It would not boot up recently, and I believe the root was heat related issues. My son likes to use it while setting on his bed - fan gets covered up and the laptop overheats. I added some large rubber feet to the bottom to improve clearance for the fan and that has helped, to a point. The laptop will boot and I can log into my son's account. After 5-10 minutes, the screen goes blank (50% grey scale, neither bright or completely dark). At that point, nothing seems to bring the screen back, so it is unusable and a hard shut down is necessary. I have cleaned it with Malware Bytes in the past and now have Microsoft Security Essentials installed, so I think/hope any virus issues have been resolved. My suspicion is that this is heat related, but exactly what is failing I do not know. Two months ago I replaced the power jack in the laptop and the power supply because of power connection problems. The battery is shot and will not hold a charge, so the laptop can not be used unless it is connected to the power supply. Since I replaced the power supply and jack, the laptop has been functioning okay. It would crash on occasion, but I attributed that to malware. I had to purge the hard drive earlier this year and restore the system because of a malware infestation. Any help is appreciated.

Have you used some compressed air to blow out all the vents/ports, especially where the exhaust port is for the fan?

Thanks for your prompt response. I have not tried compressed air, but I will and see what results I get. The fan does continue to spin even after the screen goes blank, so I believe it is still working. Would using a standard vacuum cleaner to suck any debris through the vent be helpful, or is that potentially enough flow to damage the fan?

Using a vacuum has been know to cause ESD's (electro static discharge) which can kill any/all circuitry of the system. I just use the can's of compressed air from Walmart, unless you can find a deal some where else. This will blow off all the dust build up that accumulates on the fins of the fans and vent ports. Dust build up is the main contributor to over heating. Always blow it out at least once a month and use a chill mat or chill pad.