Mac Mini 2011 no startup only three beeps - motherboard problem?

Background: I have a mac mini mid 2011, OS 10.8, 8 gb ram. It has run smoothly for the last 3 years. Yesterday it started up, but "freezed" after 10 minutes. The screen was in a fixed mode and I could not force the applications to quit or get the computer to react in any way. After a restart the computer beeped loudly three times, indicating problems to access ram. After that it run as usual for 15 minutes, and then freezed again. After a third restart it ran for one hour, then freezed. This time it refused to start, giving three loud beeps followed by a short pause, and then three more. According to apple support this indicates problems accessing the ram memory. The light indicator in front is on, and you can hear the cooling mechanism starting up just before the beep. But the computer wont start.

Today:

I´ve tried starting up while holding cmd+alt+p+r, but no luck. I've changed back to the original ram (2*2 gb), but no changes.

Is there any possibility that this is something other then a hardware error?If it is a hardware error, is there anything other then the motherboard that might be wrong?

According to my local support service the fee to see what's wrong is 90 USD, and replacing the RAM - slots (which from what i understand are attached to the motherboard) is 800 USD. This of course is money that I'd rather spend on a new computer.

Is there anything I have not tried that I possibly could?

All the best

Pär Säthil