I bought an 02 Lancer ES with the 2 ltr engine for my son's first car. Drove it home fine, and it sat for a couple of months. Naturally, the battery went dead, so I replaced it. When I tried to turn it over, I heard an electrical humming sound, but no crank or start. I replaced the starter (twice), the ignition switch, and the negative batter cable & ground. Still nothing. All of the fuses are good too. When I unmounted the starter, but still had it connected to the positive terminal, I was able to get the starter to engage by touching the back part of it to the engine block. I even got the car to start up yesterday when I simply touched the negative battery cable to it. However that was a one time deal...hasn't happened again since. I cleaned the area where the starter meets the engine, but i'm all out of ideas. I also swapped the horn ignition relay with the starter relay to see if that was the problem...didn't work. It seems like a grounding issue, but I'm not familiar with this car yet, and i'm not sure where to even start here. Any help would be greatly appreciated!!

 

If the starter is properly hooked up and grounded and you can see the spline gear move out to engage, then your starter is not the issue. With in regards to the hum, there are usually 2 different areas of hum. Under the hood and under the rear driver seat where the access door to the fuel pump is located.
Just pop out your back seat by grabbing the front of it, right underneath the lip and give it a quick pull.
It should un-pop and the other side as well.
There are just two big tabs on the rear of the lower bench seat that push up under the folding split rear back area.
Now you should see a silver metal square held in place by 4 little screws. That is where the fuel pump can be accessed from.
Turn the key on and see if you can hear a high pitched whine or hum from that location, even when someone is trying to crank the engine. If you hear nothing then your fuel pump can be bad. Espciially if it has never been changed on an 18 year old car.