Thanks for all the responses.
I did some more research after I made this thread and found out that for most camcorders that use .mts, the series of folders that the video files are in are actually code or something that the program that comes with the camera uses to play them. Where I went wrong was taking them out of the folders and just moving them to my desktop. I tried a few different converters, but I didn't like the result from any of them (the free trial versions at least.) What I ended up doing was having my friend come over with his PC and he used some Windows program to open them and save them as .wmv's, then I used mpeg streamclip to convert those into apple prores for final cut.
Basically .mts is a pain in the ass.