http://cdn.overclock.net/b/b0/b0e1cc69_Capture2.jpegFirst it will only give you 950 watts on the 12V side, the good news is that it should be enough for 4 270s.
Second, this PSU has 5 rails. Chances are you have two cards hooked up to one rail which overloads it so the PSU shuts down for it's own protection. Think of it kinda of like trying to plug every appliance you own into one outlet and turning them on. An analogy: Even though your main line (the PSU) into the home can handle it, the smaller circuit (the rail) can't handle everything and the breaker trips. You need to move some connections inside the PC around to get them split up right.