Also hopefully your psu is powerful enough to run them both.
Test each 5770 individually as your main card to make sure , you did not receive one faulty one. I'm suggesting that because you had trouble booting with both. The lack of bridge would not cause memory dumps. Just no crossfire available.
Thats weird that you didn't get one with it. I thought the cards usually came with a bridge so that you could xfire them.
However whats your motherboard?
On my motherboard you had to have an 8pin to feed the extra power to the other pci-e slots so that might be one of the reasons why your getting the blue screen. It did it to me when i tried to fire it up with both and didn't have that 8pin in there.
My XFX card did not come with a crossfire bridge either. I purchased the HIS brand cable off newegg. Not a very cool 15$ hit. I also purchased my HIS 5770 card to crossfire with the XFX at the same time, and It claimed to come with a crossfire bridge, but after the XFX cards lack of a bridge i went ahead and just ordered one, so now im stuck with 2 since the HIS card did come with one.