Sorry I missed that part about trying the onboard, that's one on me, d'oh! Also I see a reply I made is missing, this forum is acting weird again (sheesh). Anyhow I'd go with EVGA tech support on this and say it's a mobo failure/issue. For diagnosing something like this (motherboard failure) from what I understand it's a process of trial and elimination (like trying different cables, pieces of hardware etc...)
Don't feel bad or slighted that no one else responded to your post. Often on these forums people will answer if they:
1. have the time (it's free help after all
2. Have an interest in the subject (that's why you see 1000 replies to questions about the latest tech and games)
3. Feel confident that they know exactly how to solve the issue
4. Check the thread(post) and don't see the person already getting good/accurate help or advice
I have never heard of a GPU failure taking out the onboard video. Supremely weird. If you haven't already (but you probably have) try a different onboard output like dvi or vga, with no card plugged in, with a different monitor than the one you were using when it shut down.
A few things about replacing the motherboard if you have never done that before:
Your os (probably windows), any antivirus programs, games you have to register online etc. will be keyed to your MAC address. That is what identifies your computer from every other computer ever made. Your MAC is on your motherboard, so when you get a new one, all these programs will think you are someone else trying to use illegal copies. There are ways (that don't always work) to get these programs "re-keyed" to your new motherboard/MAC address via the program manufacturers but you'll have to contact each one and explain the situation.
Not a pleasant note to end on and I'm sorry if I'm the bearer of bad news. I just want to give you a heads up about some of what's involved in a motherboard swap/replacement if you didn't already know.