Eventually it happened. Yesterday, the PS3 switched off by itself, and the light was blinking yellow. I tried a few times to restart, but it didn't stay on for more than 30 seconds. Google says it's the "Yellow Light Of Death", and it's due to overheating. Apparently the console can also not recover from that.

I found a solution though, several people tried it, and it seemed to work. Heating the PS3 up with a hair dryer through the ventilation shafts for 15 minutes, then straight away cooling it down again for 20 minutes.

Tried, and it worked, it's running fine again, so I backed up some stuff, mainly savegames, because this is not really a permanent fix, it can last now for days, weeks, months to come, but probably it's somehow dead. If I get the YLOD again, I will have to look out for a new one, as I'm not gonna use the hair dryer method all the time.

I looked on eBay, and they sell used slim 120GB consoles with FW 3.55 for 180€. Might be an option, I still have hundreds of games to play on the PS3, so I really need a new one, if the old one completely dies. The slim ones also won't get the YLOD, because they are better cooled.