So, I took the Jamis to the local bike store to have it appraised, and get a list of suggested maintenance. The bike shop said that in it's present condition, the bike wasn't worth $100, and the list of suggested repairs was over $200. Add to that the price to replace the damaged parts I mentioned earlier, and it quickly became a money pit.
They recommended a new shifter (the old one was so worn it wouldn't shift reliably), chain, cassette, tires and cables. They also suggested a new stem, new saddle and new bars due to damage.
So, I ended up getting a new-to-me bike.
It's a mid-2000's (2006 I think) Specialized Allez Pro. Picked it up for $600.
I can't believe how fast it is. So easy to pedal, even in the higher gears. I am going to take it out for a quick ride (20-30 miles) and see how it goes.