PS3 display output glitching before freezing

Recently, my PS3 has been acting up.

During play (sometimes after an hour or so, sometimes at startup) the PlayStation will freeze and all kinds of graphical glitches will show up and cycle on the screen, such as the one pictured. Any musical audio will continue to play, but the console becomes unresponsive to anything except the eject button and the power button.

I have tried rebuilding the database, and just about everything in the safe mode menu. I have also verified it's the console having the issue as it happens on my other TVs and with different HDMI cables. I even tried another power cable, just to hit all of the bases I could think of.

I'm familiar with electronics repairs, but I'm not familiar with the PS3 infrastructure, so if there's something I can do to repair this, I'd love to take care of it myself.

I've read elsewhere that the thermal compound used on PS3s is less than awesome. I haven't really paid attention to the PS3's average operating temperature, so I'm not sure if that's the issue or not, but it doesn't seem hotter than your typical console after an hour or two of usage.

Hoping I don't have to junk it and get a replacement.

Note: I got this PS3 from a friend who had to replace the drive in the console as the factory drive died, but that was over 2 years ago and it has been working fine up until about a month ago.