A blowdryer, by itself, can draw every bit of a 15A circuit. I have never looked at the specs for an iron, but I imagine its not minimal due to the heating. I see no issue here other than you are overloading the circuit.
In 1994 code wasn't as restrictive as it is now in respect to GFI and dedicated circuits. There could be bathrooms, outside outlets, and garage outlets all on the same circuit and all on one single GFI. Just because the receptacle isn't a GFI receptacle, doesn't mean that it isn't GFI protected. I am guessing that you have a bad GFI or you have backstabbed receptacles with a bad connection. You should first check the test/reset buttons on all the GFI's you find. IF those all work, you need to check for 120V from hot to neutral on the load side of the GFI's. If you find power, you need to start taking receptacles out and checking for loose connections. On top of that, if you do find backstabbed receptacles/switches, you really should remove the backstabs, pigtail the wires, and connect the wires to the screw terminals on the side of the receptacles.
Answers based on the National Electric Code. Always check local amendments.