Based on the behavior my theory is that one or more of the Quicktime codecs has been damaged. FCP7 installs a variety of codecs that don't come with every Mac which gives you additional format support. You should not need to purchase that component as it is part of the FCP7 package. That suggests to me that 1 or more of the FCP7 installed codecs is damaged.
At this point I would suggest 3 things:
1. Install the combo update as a I suggested above if you haven't already (If those don't work then reinstall the last update: http://support.apple.com/kb/DL1400)
2. If you have a complete backup of your system (like with Time Machine), restore the contents of /Library/Quicktime/ from the backup from before the update was installed, restart the computer and see if it works.
3. Post your issue in the FCP7 forum and ask how to completely remove and reinstall FCP7 and all it's components (last I checked it requires a complete Erase and Install but I'm not a FCP person so ask the experts first): https://discussions.apple.com/community/professional_applications/final_cut_stud io
Side note: If the files open in VLC and you don't want to do all the above work right now (up to you obviously), you should be able to save the files out in a readable format by going to File > Exporting / Streaming Wizard. Personally I'd try to get your system back the way it was by taking the above steps but you have to balance your immediate need vs. time spent to fix this long term.
Best of luck to you!