I just bought a boat with CG documentation and will be going through this process myself soon. There''s a CG station nearby so I may be able to take care of it all that way.
On that engine--if it starts but doesn''t run, you should worry. Try putting a water hose to the water intake so it can be cooled, check the oil, and then see if it runs. If its an outboard, should be simple enough to put it in a testing tank. May be a great price because it needs a new engine!