I found a $50 bill on the floor in our local grocery store. I took it to the front desk, and they said they would hold it for 2 weeks to see if anyone said they lost a $50 bill in the store. After the two weeks they called me to pick it up. I felt a lot better spending that money after the two weeks than I would have without doing the right thing. I'm sure you feel the same.
Regarding the watch, first get actual dollar amounts on the options. How much exactly to fix it, and how much exactly would you get for it both fixed and broken. Those numbers are way to important to make the decision without that information.
Once you have that info, please rephrase your question based on the disposable money you have to pay for repairs and what stage of working toward FI you are at. Those make a different to our recommendations.
Having said all that, for myself I would lean toward having it repaired and wearing it for a while just for fun. Never had an expensive watch and might be fun wearing one for a while. But in the end I would sell it, since my idea of a great watch is more along the lines of a Pebble rather than a Rolex... :)