Hmmm what brand and type of TV do you have 780i? 1080p? This will determine the max resolution for your TV.
Sounds like you could have a couple issues:
1.) your power supply is made by Apevia which is notorious for low quality PSU's that tend to fail after a couple months....if you dont believe me read the newegg comments associated with your Apevia PSU 4/16 reviews had dead PSU's.
When it comes to PSU's the quality of the power is more important then the wattage.
2.)your connecting with an HDMI cable .....the only GPU that supports sound from HDMI is the 4870x2. I found this out after hooking my 9800gtx to a 37" Olevia TV. With HDMI cables you get no sound. DVI is the cable connection of preferance for 9800 gtx.
3.)you said it was a new build.....you may not have all the kinks out of it yet. I suggest posting on the Motherboard manufacturers forum maybe they can give you more specific help with your build. ( I recently discovered why my EVGA 780i motherboard was intermitantly failing to recognize my hard drives......turns out the Sata cables included with the motherboard are cheap and can handle being slightly bent).
4.) Could just be your TV. I had a similar issue with CTL 22" LCDs....had to return them cause they would fade to black after 1 minute of using them.....I ended up buying a Viewsonic and havent had any problems since. Does your computer work when you hook it up to a different monitor?
I just want to comment and say that I noticed that 3lvis posted a very good, detailed and researched reply. It is refreshing to see people as willing to help as this person. And to the OP: It sounds like a power supply issue to me.