okay...so this might be completely random and don't shoot me if it sounds stupid as I am no computer guru, however...
I had a very very similar problem, it would try to boot and then the monitor would go black and say something about analogue/digital... I ended up moving the pc and monitor to another powerpoint in the house and it worked, booted up fine and got my screen back. Took it back to the study and it wouldn't work. Still thought it was a power problem with my pc...
I took it to the pc shop and they said it needed upgrading and had a couple of issues so got those fixed, took it home, booted up fine for a few days then did it again!!! Pulled the power point out and it was full of ants and the connections were eroded...new power point and it was good as gold!!! Fortunately I needed the upgrade and glad I got some of the other issues fixed as it was buggin me!!
Like I said...may have absolutely nothing to do with it, but an electrician friend of mine came over and checked the voltage on my powerpoints and three of them had a reduction in voltage due to corrosion so he replaced 3 of them for me!!
Just an idea!!!