Composer fee for unfinished film

I am trying to figure out what to invoice for a piece of music I wrote. A film maker friend brought me in on a project she was working on. The film was unfinished and she really needed music. The finished film would have been 3:30.

My original quote to the production team was $100 per minute for finished music, and I would have done two rounds of edits. The production team was aware of this quote, but there was never a formal agreement about this rate.

I wrote music for the unfinished film and the producers ditched the film, which included my composition. They are willing to compensate me. It's a matter of me telling them what to pay me. I'd be interested in working with them again, so I feel hesitant to charge my original rate, since they ended up ditching the film and the music.

Question is: stick with my rate or charge some type of flat fee, since they didn't use the music?

Well, they asked for music and you composed it and put effort in it. 

But I am not familiar with the money business in compositions yet.

Charge them a lesser rate, but get it in writing that you have full rights back to the music, so you can adjust it and re-use it with a future project as you see fit?  Lets them off the hook a little, doesn't completely throw you under the bus, and gives you a good reason for the discount so you look business-like, and not like a pushover?  

I'm with pateceramics. You did the work, but you want to maintain good customer service at the same time.