Hi,
Some suggestions to try:
1. Try a power reset -
Remove the battery from the camera
Turn on the camera.
Press and hold the shutter button for a minute or so. (This is to discharge the internal, non user removable back up battery. This battery maintains the settings in your camera when you remove the main battery).
Release the button and switch off the camera.
Re insert the battery and switch on the camera.
Try turning it off and see if it works correctly.
If it does you may have to reset the date and time settings etc., as these will all have defaulted to a factory default setting. Allow the backup battery at least 24 hours to recharge (from the main battery) before removing the main battery again.
2. If that didn't work, have you got the latest firmware installed in the camera? It may be that the firmware has become corrupted. Even if you have the latest firmware version installed try installing it again (I don't know if the camera will allow this or whether it only permits updates) and see if this resolves the problem.
Here is a link to the firmware for your camera.
http://www.olympusamerica.com/cpg_section/cpg_downloads.asp?id=107