If you bought EfLC on disc then you have to use the EfLC launcher on the EfLC disc. You can't just switch over from the GTA IV disc. The Complete Edition is just the same retail discs (two for GTA IV and two for EfLC) that you'd buy seperately. As Mkey said, the switchover screen on GTA IV is solely for the downloadable versions of the EfLC episodes. There are no official 'patches' to alter this in any way.
Think about it. If you could switch over to EfLC fron GTA IV without changing discs, then why bother buying EfLC in the first place? Everyone would just download a dodgy copy (and product keys) and run the game using GTA IV's SecuROM.
Hope this clears things up.