Pictures, Model and serial numbers would be a good start.
You can go to Marine Parts Plus Mercury Serial 39 1 CYL 815749 and get a parts breakdown chart to help see the parts and the order that they go together.
As for the gear being in backwards ..... I am not sure it can be assembled with it backwards.
When you say the motor fired one time......how long was it running before you tried to shift it?
Hope this helps some.