Well, isn't that a coincidence!
I laugh because I just had the exact same problem with a new IP35 Pro board last weekend.
Bought the board at Fry's about 5 months ago to use for a planned system upgrade.
Same issues, no display, keyboard lights don't come on, C1 post code.
As suggested, I tried all the troubleshooting methods, minimal hardware, board out of case on the box, a stick of Kingston DDR2 667 Valueram, etc.
I build several systems per year so I had a few working alternate parts on hand to try, and I swapped out everything including the cpu and power supply, videocard, memory, etc.
Did a full cmos clear several times, removed battery, also tried a new one. Nothing worked, the board is still "dead".
After two days I gave up and ordered a Gigabyte GA-P35-DS3R. My old trusty DS3 still works flawlessly, so I felt this would be a sensible replacement. Don't know what I was smoking when I bought that Abit board.