I recommend you have a look at the current PSU you have How much over all wattage it states it can output, and a close look at the Amp rating for the twelve volt rail, or twov 12v rails each with its own amp rating If one or both added together are less than 42 or more amps.
Then you are looking at a new power supply of a higher wattage and amp rating to get the system to boot, and not freeze at the post screen or freeze when trying to enter the bios. If the supply is week it will freak the board out locking it up.
Due to the lack of required wattage and amps, if it happens when the only bit of hardware added was a GTX 770 card it speaks for its self.
The old question what was the last thing done to make it go wrong. you put a new card in that requires more power. and proved the point yourself it power related because the 560 card requires less power to run in the system and it worked ok when swapping back to the 560 card. Makes sense. Logic.
NB: check that the eight pin 12v block from the Psu is connected to the eight pin power phase of the board it will be located near or around the cpu socket.
If you missed it , or only have four connected make sure eight are fitted.
Four will not cut it, if the wattage and amp ratings are above what is needed.
That will cause a freeze of the bios if not connected again because of the extra power required so not having the full eight pin will cause the freeze ok check it.
If the board only has four pins. Then it can be a problem in respect to not enough power can be provided to run the GTX 770 card when placed in the PCI-e slot of the board.
Just hope it was a missed power connector. if the Current Psu you have is up to the job. Or the mobo simply cannot provide enough power to the Pci-e card slot.
That mean it freezes because it cannot see the 770 in the Pci-e card slot due to to much power draw with only four pins of the board provided. means a new mobo with eight pins.