Trip reset when car is turned off......and other things
 

We have a 2004 Mitsubishi Outlander. Tonight when we went to restart the car it started fine but the radio was not working, the dome lights weren't working, neither was the power locks or locks with the clicker. The clock also was not working and the headlights would not stay on unless the key was in the ignition. But strangest of all the trip was reset which only happens if you manually reset it or the car loses power. We went to an auto shop and had the battery and alternator tested and both tested fine. We then came home and checked ALL the fuses; 2 were bad, the dome light fuse and the radio amp fuse. We replaced these, restarted the car and everything was working again but when we turned the car off again, the headlights would go off but if you took the key out and turned off the lights then turned them back on they came back on. I am not sure if the trip reset again because it was still at zero and I didn't want to drive it around the block and go through the whole process again because it is getting late. My question is: Does anyone have any idea what could cause this? I am really confused and am not sure where to go next and do not want to spend a bunch of money for someone to just look at the car and not be able to figure it out. Any help or ideas would be great. Thanks.