Possibility 1: The launcher is checking the wrong spot for the game and so it fails to launch.
Press the Windows button and R at the same time (launch Run.exe).
Type regedit and press OK.
Navigate to HKEY_CURRENT_USER\SOFTWARE\Blizzard Entertainment\Diablo II.
Double cick on the key InstallPath.
Set the Value data to your D2 folder (not your PD2 folder).
If your path ends in ...\ProjectD2, delete that part.