Car lost power while driving

Sounds like separate issues, all cars can have issues. It may be your IAC motor valve located in the throttle body housing if equipped. It allows air to enter the engine while your gas pedal is not being pushed on. By you pushing the pedal it cranks because you opened the throttle plate aloowing air into the engine and when you remove your foot from the pedal it looses its air and dies, I would follow testing procedures (Repair Manual) for your car and test it and check your connections and wire harness to it before just replacing it as its on the high cost side and you do not want to spend money for part that does not fix it, this is just my interpretation of you description given, it could be other issues or a related issue to the IAC like ECU or Wire Harness or other equipment so read or watch youtube for testing steps and rule it out or in. HTH

The fact that once the distributor was replaced the car was OK makes me think that your getting condensation inside of it /// I was not aware they still had distributors on a 2003 Mitsubishi Eclipse GT