Water Heater Won't Start

Ok now let's get down to trouble shooting this! It's easy if I'm right in thinking it's a intermittent pilot system which was very common 20 years ago.
First get out your multi meter and set to volts a/c.if you don't have a digital one we are going to be looking for 24v a/c so set your range accordingly.
Now if that fan is running it knows it needs to fire up but can't. You said the pilot was lit. So.

Put one lead to ground (the water line will work or gas line)and check for 24v at both terminals of the pressure switch (sometimes they are called a air proving switch).if you only get voltage on one side of the switch then everything I already said is the culprit. If you get voltage at both terminals then carry on.

If you're water heater is the type I'm thinking the gas valve should have three terminals on it.
MV-main valve
PV-pilot valve
MV/PV-which is the neutral for the two.
Again with your meter one terminal to ground (gas line will obviously be easiest here)the other to PV. This will show 24v because your pilot is lit. I guess that's just for practice haha.
Now ground to MV. If you have 24v at the MV terminal your gas valve is bad. If you don't your ignition control module is bad. If it's an original it's probably a grey box made by Honeywell. Could be black also if it's been changed at some point.
Also I should have mentioned that although we are looking for 24v you won't se it everywhere. It could read 27v or at the valve if it's trying to open but can't it could 12 or 15 or whatever. Hope that makes sense