What would cause my "service engine soon" light to say on after the car is off and the key is removed from the ignition? Also, where my mileage is displayed, there is a bunch of dashes that say illuminated as well.
Sounds like a cluster fault. Try disconnecting the battery for 5-10 minutes and re-connecting it to re-boot the cluster. Verify that the electrical grounds to the chassis and battery are in good shape, clean and are not corroded.
The "*" in the cluster at initial power on is normal. However, the "*" should go away after a few seconds. The check engine light being on after key removal is not normal.
Suspect a problem in the ignition switch (cluster getting power while PCM does not). Does the battery drain?
Take the car to an auto parts store to get the DTC codes read. Post the full codes. Do this before reseting the battery.
Pull Fuse F2.5 and then F2.34 in the Central junction box. Report which fuse pulled makes the cluster go dark.