1. I don't know about a PBEM mod. You can PBEM without any mods.
2. You should not
move any of the any of the files or folders.
3. If you still have the files/folders that you moved, move them back to from where you moved them and everything will work as before.
4. If that doesn't work, find the "General.opt" file. It is installed in "c:\Program Files\AGEod's American Civil War\ACW\Settings\General.opt" per default.
If you modified the default setting during installation you might have installed on a different hard-drive than "c:", in a different base directory other than "\Program Files\" and with a different installation directory than "AGEod's American Civil War\". But since you moved some of the files and directories around, I assume you know from where and to where you moved them.
At any rate inside the "General.opt" file you can find the key you entered after installing. It's on the line starting with "Serial" toward the bottom.
If you couldn't get everything moved back to where it belongs you will have to try to uninstall what you have left, clean out the rest manually and reinstall using the key you saved from the "General.opt" file.
PS Put the key in a save place so you don't lose it again