2000 Mitsubishi Eclipse Engine is not turning off

Do you have an immobilizer on your car?

That may be your problem, try this, take off the negative battery cable for about fifteen minutes, this will reset everything, then put the cable back on, and see how it goes, if that doesnt work, you will need to have a shop look at the remote starter.

Is there a check engine light on?

Ok another think that will help us out is to have the computer scanned for trouble codes, bring it to autozone and have them scan it(its free), jot the codes down and bring them back to me, do not take any suggestions from them, as they usually do not know what they are talking about, they just want to make a sale, bring the codes back to me for further diagnosis, I still want you to take the negative battery cable off for fifteen minutes too, just to see if that will help

Your welcome