Problems coming out of hibernate mode are usually PSU related. In your case, I would probably try to replace it with maybe something like this:
SeaSonic S12II 520 Bronze 520W ATX12V V2.3 / EPS 12V V2.91 80 PLUS BRONZE Certified Active PFC Power Supply $59.99http://www.newegg.com/Product/Product.aspx?Item=N82E16817151094
You can always set it so that your computer doesn't hibernate, but I don't know if that's something you want or not. I'm guessing the system probably seems to run fine otherwise. Regardless, the PSU is probably on its way out, and I would recommend replacing it sooner rather than later since it is an Ultra PSU, a brand I don't consider to be reliable.
Edit: I have heard of cases where certain motherboards have problems coming out of hibernate mode. I'm not sure if that factor is in play here, but maybe someone else can come along and provide some insight into that.