Mitsubishi Repair Problems? Ask a Mechanic for Answers ASAP
Have you checked the two fuses in the yellow "box" captive in the under hood fuse panel? These two are often overlooked since they are difficult to get to, but a failure here would cause your exact symptoms.If you have not, grab the yellow box and pull up hard while wiggling fore/aft and it will pop loose and then you can use needle nose pliers to remove the fuses from it for inspection.
Please take a test light and ground it then probe the metal tabs on the top of both of those two fuses, tell me how many tabs have power with the key off and how many with the key on.