Mac pro memory

SO my mac pro recently stopped turning on. It wouldn't startup and only had the little blinking indicator light flashing- the light above the on button for the computer. I tried moving the memory around to different slots and risers because I looked at the LED diagnostics and they were lit up on all the memory. I had 4 1g cards installed, 2 of them were apple and 2 are 3rd party. Oddly my computer sprang to life when I placed only one memory stick in slot 1 on riser A. It will not turn on if I put any more memory than that in the machine. All the 4 sticks of memory work because each one works on its own when put in slot 1 riser A. If I add ANY other memory than this one single stick it stops turning on and gives a sad flashing light.

No other LED diagnostic lights are lighting up. It does give scrambled pages from the internet from time to time, but otherwise it is fully functioning with a lone 1g of ram. I think it's the logic board that is finally failing. I have a 2008 model with 2.8Ghz so it is out of warranty and getting it to the apple store is a giant pain as I live in a major metropolitan city and it would mean a long trek on multiple modes of public transportation. Does anyone have experience with this sort of issue or know anything else I can possibly try? I'm really tempted to just sell this machine as is and move on with my life, but I would like to try every option before I reach that point.