To start off, I have a 80 gig fat PS3 and I got it around January of 2007. So just a few minutes ago I was playing Skyrim for about 30 minutes, and then my PS3 just shut off by itself! After it did the red light kept on blinking and I heard some sounds that were coming from inside the PS3 when the light was blinking. This has happened to my brother about 3 times today and we haven't touched our PS3 since 2 P.M. today. Is my PS3 close to getting the YLOD? Lastly, my PS3 is in a good ventilated area and I always keep my vents on my PS3 clean.
Since your PS3 is that old, your PS3 is probably overheating due to dried out thermal paste. You can replace it yourself and your PS3 will probably run properly.
I have written a guide that can take you through this process step-by-step. If you are interested the link is below:
I have the same problem as yours... however when i play a game fron the Hard drive, it does not shut down suddenly, only on disc based games. So yeah overheating is the issue here i reckon. Were u able to fix your ps3?