Read ECM codes. Very likely have at lest one.
Engine high idle and MIL on can be ECM trying to make E power for iffy wiring, Alternator or battery.
Test volts at battery before during and after starting the car. Charge bat = 12.6v, engine running should be ~ 14.7v
pull lighter socket and disconnect it before replacing Bat fuse and maybe others w/ right fuse(s).
socket can rust or things fall into it causing problems. See my Cave,
LighterIf right fuse blows still have other problems maybe harder to find.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)
The Ogre's Fiero Cave