Hi,This is risky business, not responsible for damages on your end. We keep going until you're satisfied. I come and go. be patient
You are correct in your diagnosis and cure.. its just that there is still ice in it. The pressure switch is open because the combustion blower is not able to pull the slight vacuum required due to its exhaust tube blocked with ice.
hair driers are slow.. hotter driers can damage the plastic vent parts.. some mfgrs recommend using hot water over the frozen parts. Others recommend low wattage electric heater pipe wrap **RATED FOR USE WITH PLASTIC PIPE** over the full run of the vent pipe and insulating over it with fire rated fiberglass pipe insulation... there are local codes on that. It will be best to check with your local city plumbing inspector before you proceed.
If the vent piping is short you may want to consider boxing it in..
Let me know how this looks on your end, we can go from there, Phil