Instructions
Make sure your copy of "Oblivion" is up to date. If you do not have version 1.2.0.416, you will need to download the latest patch.
Make sure your copy of "Oblivion" is not from Direct2Drive, because OBSE will not work with this version of "Oblivion" because it is encrypted. No-CD hacks may also make it impossible to run OBSE.
Check the folder you installed OBSE to. It should be the folder that contains the "Oblivion.exe" file. If you are using a copy of Oblivion through Steam, this will be in the "Steam/steamapps/common/Oblivion" folder.
Download the patch from the OBSE website and run it to update your version of OBSE.
Open the "Oblivion" folder and open the file "obse_loader.log." If the error listed there is "could not find checksum," you may need to uninstall and reinstall "Oblivion."
Launch "Oblivion" by using the OBSE launcher to make sure OBSE is running. If you have a copy of the game purchased through Steam, launch the game through the Steam launcher.