I know I keep banging on about it, but you NEED to try the onboard video.
You originally mentioned that the PC makes at lease some noise when it boots (even if thats fans) yes it could be the MOBO and it could be the PSU, the CPU, GPU, Northbridge or Southbridge that have died.
just try the onboard and then i'll be happy :D and if it still doesn't work, get the parts out of it and reuse them/sell them to fund some if not all of your new build :)