Well I don't think the platen can be at fault because I can turn that star wheel by hand and the platen moves. The levers just don't seem to move as far as they should when typing.

getting closer. Feel free to help.  

Its not downward pressure that makes it work its actually pressure to the left. So this leads me to believe that either a spring isn't working or the carriage release is always in the release position, which seems congruent with the fact that I can push the platen to the right even without using the release lever. And when it fell upside down it very likely could have fallen on the carriage release lever.

That spool is the main-spring which drives the carriage and the string is called the drawband which pulls the carriage from right to left. All mechanical typewriters have these, some are more durable than others, but the principle is the same. That machine is going to have to be taken apart enough to get access to the spring, re-tension it and re-connect the drawband. This is a good opportunity to replace the drawband, which is most likely over 40 years old. 
Sounds like this machine needs professional repair. If you feel mechanically adept, you may be able to do it, but be prepared to have a decorative bookend or doorstop, if you don't get it right. Good luck.
Phil Forrest
 

Ugh...after taking out everything above the spool I realized all I needed to do was remove 2 screws on the underside to get the spool out. Dohhhhh!

Any tips on getting that spool set up properly Phil? The spool is spring loaded so I'm hoping if I slide the carriage all the way left then wrap the spool so there's no slack and then install it, it will produce the proper tension. But I'll bet there has to be some tension on it when I install it, and I'm not sure how I can do that, or if I can do it.