Since you have a green light that tells me there is voltage ,some gfci’s require the test then reset reset to be pushed to activate them I would try that first.
One of the things that goes wrong quite often with a overloaded circuit is a connection point fails some place in the circuit it could be on the hot or neutral.
A common source of the failure is a back stab. These push in connectors get hot and may loose contact or direct contact with the wire in some cases leaving only a carbon path or a very light contact that may power a radio but not a light bulb. You just replaced the GFCI so it is time to work back towards the breaker panel.
I would use the hair dryer and start plugging in at the other receptacles on this circuit. You may find several that won’t power the hair dryer in older homes.
Once you find a working receptacle on that circuit it will be that receptacle or the first non working receptacle that has the bad connection.
It may also be a broken wire or a wire that came out of a wire nut and last it could be a bad connection in the breaker panel. We normally work back towards the breaker as this is how homes (under the NEC) are wired. If a room has a common wall the receptacles in that room are on the same circuit most of the times in older homes.
I find the backstabs ~96+% are the culprit. I mention this because you have a green light on the GFCI and on all the ones I can remember are green when properly connected.