Many years ago I had a similar problem, I don't think you have it though but for me it turned out to be the graphic card that was just a little from actually touching my motherboard or maybe half of the pins were connected.... It resulted in a PC that basically worked but the screen wouldn't show anything.
Like I said, I don't think you have it but just saying, make sure your graphic card is as far as it can go inside that thing.
Wattage is not the only concern when powering a GPU you need to have at least 30A on the 12v rail for a GTX560 and the OP has that. So i highly doubt it is an issue with the PSU and more likely to be connections or motherboard problems.
Are you sure the card is "locked" into the PCI-E slot?
Did it click into place when you pushed it all the way in?
If you can answer yes to the above then you should try swapping round your 6+2 power leads on the GPU, I once had a computer that would not boot with the cables plugged in a certain way. This was a PSU faulty for sure but it ran fine the other way for years :P
If you are still no further forward try removing your battery from the motherboard and resetting the cmos. Hopefully this will kick start it and get you going
You could also have the problem I did. My motherboard came with a bad pci-e slot. I tried it in a different slot and worked. I also tried it with onboard if your board has it. Just something else to add to the possible tests.
ok so there is 2 different spots right next to eachother to put the 6pin pci-e plug from the psu in. does it matter which one? also the 6pin has a +2. does that need to b plugged into something? the gpu fans are running. the light on the card goes green when the pci-e plug is plugged into it..i took out the card and put it back in (pain in the ass bc the card is so big)
You need to plug 2 of the 6 pin power connectors into your GPU not just one. Both sockets on your GPU should be used. If your PSU doesnt have 2 then go into your GPU box and use the molex > 6 pin adapter provided