I seriously doubt the adaptor is the issue, particularly if the PC doesn't even beep at POST (which you don't see). Why don't you start from scratch and test your components outside of the case? Keep only what's needed to test it (motherboard on a non-conductive surface, CPU, one memory module and video card only). Connect the CPU, ATX and video power cables from the PSU. Then jumper the power pins on the motherboard (front panel connector) and see what happens.
Building PCs may be fun, but having spare parts definitely makes it a lot easier to fix issues.