Clutch drag!! Just put the chain on, it will be fine. Clutch drag will always cause some rotation of the output shaft if there is no load..
EDIT: oops, after re-reading your post, I shot you the wrong way. That certainly sounds like the trans has issues and either assembled wrong or a gear has welded to the shaft. You might find a gear where the bike will not die when the clutch is released. That is likely the gear that is welded.
You took the clutch cover off, why? Am I missing a chapter here?