You might try to have a look under the sliding cover. It is just a piece of plastic, sliding in two grooves of the main body.
Except that it actuates a small lever to inform the camera of the position of the cover.
So, you can take it off by prying it open from the top or bottom edge. Just remember to have the cover and the small lever in the same position when you re-assemble the cover. Hopefully you will discover some accumulated gunk that might interfere with the proper operation of that small lever. And/or squirt some contact cleaner at the lever, hoping it will penetrate below where the electrical contact is; try actuating back and forth, check that, with battery present, the lens reacts accordingly.
Good luck. Or should I say better luck. Mju-II my favorite subcompact, nicknamed The Soap Bar.