First, thanks for the help..
Now quick update, I tried to just reconnect everything back and see what happens..
It started to work again! But the problem seems to be in the fan speed control switch (or blower motor switch), not with the slightly melted electric connector that connects with the vacuum switch.
certain speeds work and then just stop working. When I put some put some pressure on the connector behind it, it goes on and off.
Should I get a new switch ? http://www.jeep4x4center.com/switch-...5011214aa.html
And should I replace the resistor too ?