|I had the exact same problem for over a year, where sometimes it would work and other timese the 3 beeps with the yellow flashing.|
When the PC did start every now and again it would also freeze and nothing would work, when I rebooted the 3 beeps come back.
I cleaned the fans and dust bunnies and it worked for a while. Then it stopped again, then I found the battery was flat, which I replaced and it worked once then stopped on the next reboot, so after looking at this post and found that it is NOT a Mothorboard problem but actually a RAM memory contact problem and after cleaning the points of each RAM chip with a pensil rubber and whipping it clean it was very dirty / Green carosive grime that was removed.
As soon as I did this the PC started normally, and then I rebooted again and all is well. Best advise I have read so far.