I have a quite similar problem here. My PS3 suddenly turned off with 3 beeps after a few minutes of gaming. It was obviously not linked to overheating since after a couple of hours of cool down, it would immediately turn off with the 3 beeps and red light blinking right after trying to turn it on.
I managed to eject my GT5 disc via a fan test (hooray!), but my PS3 is still dead. I bought it in 2008 so the warranty is way expired, but I'm not particularly confident in tearing it apart and fix it by myself. It looks easy on YouTube, but it might turn into a nightmare with my cat messing with the screws and wires!
I think imma buy a scarlet red PS3 slim, but I'll wait till E3 for any price drop announce. My biggest concern is how to use the data on my 500gb hdd without losing all my progress, garage...