Yeah, I got the exact same problem. Now though, I can at least get the PS3 working for couple minutes before it goes. CRAZY VIDEO FREEZE and still hear sound working.
Here's my history if this can help you or anyone reading. (PS if anyone does fix this, please PM as well.) So got the PS3 from my friend cause it worked for a while and then went hot and froze video. eventually, the unit then afterwards wouldn't even turn on. Light stayed green, DVDs would pop out, etc, but only to shut off would be hit the switch in back. Yet, I noticed it was pumping a load of heat out the back and the fan was working way harder than as it was on a normal functioing PS3.
I opened the unit to try to inspect if there were burn marks or misconnected wires, none. I kinda thought this might be the same issue with Xbox's RROD. Scraped off the old thermal paste, put some new. WORKED LIKE A CHARM!!!
Played Kingdom Heart II for a couple hours, and to check it was not a fluke, I turned it off. Turned it back on, sound, no video. I kept turning it on and off for maybe a half hour and got tired. I came back to the system a few months later (I've had this since Christmas btw.) System was still acting same way sound, no vid.
I tried now the Arctic Silver trick. Exact same situation, worked beautifully for a few hours but the video was grainer this time (I was also playing a PS1 game) Turned it off and turned it back on, Startup came on but kept freezing after a few seconds.
There's where I am at now, I can't pinpoint what hardware it could be, but overheating is a definite issue.
Sorry if this doesn't solve the problem, but i'd rather pinpoint what it is in the first place.