The starter is most likely bad, it probably has a bad armature winding or commutator spot. Again, this is a guess. No one can tell you for sure without looking at the vehicle to diagnose it properly. The piggy back solenoid grounds through the starter armature windings on all starters except for the fork impelled starter drive types like some old fords.
The brushes in the starter are worn out. The old tapping on the starter is what you do to get it started one more time to get it in the shop for a new starter.
If the small trigger wire on the starter solenoid is not corroded and is making good contact just replace the starter. The ignition switch and neutral safety switch is working since hitting the starter makes it work.
The first thing I would suggest is to check all of the connections at the battery starter and the alternator make sure that they are clean and tight if that checks out it sounds like a starter but to be sure try to get it to you closest auto parts store or just bring the starter and have that tested but I think that you just may have a bad starter
Not exactly sure but it sounds like the starter solenoid. It's a common problem, not just with Mitsu but with all cars.
OK I have a 2001 eclipse 5speed I just bought it from some dude about a week ago and today when I tried to go to work I would turn the key nothing would happen no sound or clicks the light on the dash and head lights turned on fine then I tapped the starter with a hammer and tryed agian it started and it lasted about two days now tonight it did it agian tapped the starter and starts but Im not sure if its the starter or some other failure