GFCI installation help
OK, stop.  Put it back the way you found it; it was that way for a reason. 

Since you don't even know what LOAD does exactly, you don't really have a reason to want to use the terminals (other than "gotta try random stuff til it works").  Don't ever do that with electrical -- you will find many combinations that will work (mission accomplished) and will create a lingering problem that will kill you. 

Your first problem with this GFCI happened because you attached the wires to LOAD instead of LINE. That was a mistake from removing the warning tape unnecessarily (or getting one with the warning tape on the wrong terminals; that has happened). 

Your second problem was because the downline wiring is not compatible with a GFCI, which may be why the original installer used pigtails. Whatever: It's not your problem today; you're not here to chase that problem.  Be good to fix it someday, though. 

Now, you said you hooked it up exactly as you found it. I'm guessing you were looking at the physical dimensions, e.g. which side has the ground.  That throws people all the time, because it's just not consistent among devices.  You need the LINE side (which means don't take the warning tape off the LOAD side). 

If that doesn't work, either this GFCI is defective, or there's a line problem upstream of the GFCI, e.g. the original problem was not this GFCI.