GFIC outlet indicator light is green but no power in the circuit
If you don't have a non-contact voltage tester you should buy one to help solve this problem.
Start at the breaker and make sure it is on for the problem circuit. Remove the faceplate of the GFCI and carefully check for voltage on the "Line" side of the GFCI. Assuming there is voltage on that side now check the "Load" side of the outlet. If the green light is on you should have voltage there as well. If you do, continue downstream carefully checking each outlet as you go. Remember the circuit is live.
The problem will probably be in the first outlet with no power or possibly in the cable between the last outlet with power and the one with no power. Once you find it, shut down the power back at the breaker. Check the GFCI to make sure you have turned off the correct breaker and there is no power in the circuit. Then  check the connections to the outlet particularly the pigtail. A loose pigtail at that point would be the prime suspect. In these cases the problem is typically something basic like a loose connection. If this is the outlet where the hair dryer was plugged in and the connections on the outlet and the pigtail are all tight, I would replace the outlet. They are inexpensive and not worth fooling with.
Turn on the breaker and test for power again. My guess is you will have power at this point. If not, the problem, unfortunately, is going to be in the cable between the GFCI and the first non-working outlet. In which case it might be time for an electrician.
Edit
Forgot to mention backstabs. Check for them. They are notorious for arcing and failing. Alaways better to attach wires securely with the contact screws.