Oh, AMD theres your problem right there. JK

Just out of curiosity, where was your graphics card before you moved it and why did you move it? Was it acting up before and you moved it or just because?

As for your GTX560 temp...45 isnt overly high. My GTX570 currently running at 40 on idle with all case fans running at lowest values so 45 isnt too high, as long as its not hitting into like the 70s or 80s under load there isnt much to worry about there. Also could be because if the PCIE slot you moved it to is any closer to the CPU/ cooler it would restrict some airflow across it and keep it next to another heat releasing component.

As for BSODs, what are the stop codes? Make sure in your BIOS you have it set so that it waits for you to press a key before restarting on a BSOD. That way you get to write down the code. What the code says or post it on here and someone may be able to give you a better idea.

Also, when was the last time you cleaned the dust out of your computer? Dust can have a HUGE impact on computer performance.

However, if i had to guess what was wrong I would have to say your mobo is probably dying. I only say that because I had similar issues with a MSI board on my last computer. For no apparent reason it would BSOD from a thousand different reasons. I wasnt once able to get a stop code to come up twice, it was a different BSOD every time. So hopefully for you, only one or two stop codes repeatedly show up so you can narrow down to what it might be.