I would start by removing and reinserting the battery. Then, if that doesn't do it, try what careyana suggested. If none of that works and you are still having issues with all that, you may want to use the wipe handheld command under options >Security Settings >General Settings. That will erase all your personal data (contacts, emails....etc.) but leave your OS and apps untouched. You should do a backup first, however, but don't restore it after the wipe. Then go back and setup email again, etc. You can then add back individual items from your backup. I suggest not restoring the entire backup as you may just get back all your original problems.
If none of this works then you'll have to wipe the handheld completely of data and OS and reload the OS and start from scratch. Let's hope it doesn't come to that but if it does, it's not that hard to do.