Overheating

Yes, you have a blown head gasket. Have a leak down test done to confirm.

Roy

Leaking cylinder head gaskets often does not show up with a pressure test, especially after the engine has cooled down. The best way to identify them is with a "sniffer" test. That involves drawing air from the radiator through a glass cylinder with two chambers partially-filled with a special dark blue liquid. If combustion gases are present that liquid will turn bright yellow.

When combustion gases leak into the cooling system fast enough they can pool under the thermostat and prevent it from opening. Thermostats open in response to hot liquid, not hot air. That is likely what started all the trouble. Your radiator fan may indeed have been bad but it is not needed at highway speed. A fan that does not run will not cause overheating at higher speeds when you have natural air flow through the radiator. A leaking head gasket can cause overheating at any speed if the thermostat closes and blocks coolant flow to the radiator.

The two additional clues to a leaking head gasket are the temperature gauge going up and down as the thermostat repeatedly opens and closes as the air pools under it and it gets hit with hot coolant sloshing around, and the reduced circulation brings less hot coolant into the heater core in the dash so the air will not be very hot.

Leaking head gaskets are common on many car brands and it can happen on much newer ones. There are a lot of variables in the cost of repair but a guess would be between $500.00 and $1,000.00 which is a lot less than a few months worth of new-car payments. Your mechanic will likely also want to replace the timing belt. It will be off already, and if it breaks the cylinder head will have to come off again to replace bent valves. Honda used to recommend the belt be replaced every 75,000 miles, and they typically broke at 65,000 miles leading to a lot of expensive repair bills.

I personally would rather stick money into a 2002 model anything than buy any newer car. Some of the new technology is nice but a lot of it is inappropriate for cars. That is why I refuse to give up my 1988 Grand Caravan. I have three newer vehicles but I do not trust them as much to get me back home. Look at how much trouble we have with home computers. Cars may not let you sitting on the side of the road as often as they used to, but look at the expense people go through when a computer failure causes things like no power windows or lock, or the heater system does not work right.

PCV does not effect overheating or cooling fans.

Roy

What happens after the fan kicks on? Does the temperature continue to rise and the fan keep running or does the temperature come down and the fan shut off?

As I suggested early on, have a leak down test done to verify. Do not use the shop that told you a PCV valve.

Roy

If you are sure you got the coolant full and all the air out then you likely have a blown head gasket from the previous overheat.

Most definitely. Head gaskets can be hard to verify sometimes. They can blow in may different way. If you have a small break between the cylinder and a coolant port it will push hot exhaust gases into the cooling system. The best way to find it is using an exhaust analyzer and looking for hydrocarbons at the radiator cap with the engine running.

Check items in picture the condenser fan is coming on when A/C is on.

The head gasket is bad. The exhaust side of the head gasket is leaking.