Is a mounting post is shorting out the motherboard. DO NOT BUILD IN THE CASE when you are in this position. Start on cardboard and use the bare min parts to get to POST or beeps.
Sorry no. The clues do not point to exactly what's wrong. We'll have to work this like any Dead PC by making it as small as possible.
My computer has decided to not post to anything, be a monitor or mouse from front or back ports, but it most definitely is running because the fans are on. I have tried the following to fix it and all have not worked:
Replace the motherboard
Use an old CPU of the same socket
Use an old compatible case
Change the amount of RAM
I know that the GPU, RAM and power supply work fully because I tested them with another computer in my house and everything posted/worked.
If someone could tell me what specific part (/combination of parts) isn't/aren't working, then it would be greatly appreciated.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic