My guess is if you've overwritten image files on your computer that there is no way to retrieve them. It's strange that you received no warning.
However, you may want to try a photo recovery program and try to get some of them back off your memory card.
I believe most cameras have an internal battery that saves camera settings and works independent of any batteries that are inserted into the camera. It sounds as if it is no longer working.
Have you tried reconditioning your batteries? Doing so may revive them to hold their charge, unless they are just plain warn out and need replacement.
You seem to be having a lot of problems with your camera, so it may be time to get a new one. Why risk losing precious photos because the camera is not working correctly?!
But call Olympus first to discuss possible repair. Prices of digital cameras have come down a lot, so depending on the cost, repair my not be worthwhile for an older camera. If you decide to call them, also tell them what happened to your images. They may have a solution.
Related reading:
Photo recovery
www.digicamhelp.com/processing-photos/photo-recovery/index.phpConditioning batteries
http://www.digicamhelp.com/accessories/batteries-chargers/rechargeable-batteries.php