That is one hell of a call. I thought about it right as I read your post lol.
it's a mistake many people make, pairing an older Cougar Point chipset with IB without updating the BIOS first to account for compatibility. for now, that's the clear & likely culprit. it could be the memory's incompatible with the board as well, he/she forgot to plug in the power connector to the GPU/CPU, plugged the DVI/HDMI/VGA to the onboard port instead of the GPU, bad DVI/VGA/HDMI cable, or simply a bad, though kinda working board or a bad CPU at worst. the latter two is unlikely but could happen, i guess.
before you actually buy/replace the board, you could send it to a shop and ask them to update the BIOS. i reckon this'd be a lot cheaper to do, hopefully.
if that's not an option, then you can consider replacing it with a new board, preferably B75 or H77. BUT, make sure your board supports the CPU out of the box or is a more up to date revision with the latest BIOS pre-installed. some of the more recently released IB CPUs like the 3330 would still require a BIOS update in most boards, unless there's a new revision of the board. so far, i see B75/H77 ATX boards from Gigabyte are about the only ones that supports the i5-3330 out of the box