wavewuver,
After you have tried the drive outside the case (i.e., not screwed into the bracket) and eliminated/corrected the cable position as a problem -- and assuming the drive works properly when not physically mounted -- then take a look at the mounting screws.
If the screws are too long and screw too far into the floppy drive case body, they can cause the exact problem you describe. If that is your situation, try the shortest screws you have when you mount the drive.
PS: Floppy cables can be installed at least four ways, three of which are wrong

Make sure the section of cable with the crossed over portion is positioned closest to the floppy drive, and that the notch on the connector is properly oriented.