Use Disk Utility to repair your permissions.
Then download Preference Manager from Digital Rebellion (free) and use it to trash your FCP preferences. They will be set to default the next time you launch FCP.
Thank you so much for your prompt reply and suggestions. I repaired permissions through Disk Utility and then trashed preferences through Preference Manager, but FCP still crashes upon launch. This is the first part of the crash report:
Process: Final Cut Pro 
Path: /Applications/Final Cut Pro.app/Contents/MacOS/Final Cut Pro
Version: 7.0 (7.0)
Build Info: FCPApp-906181654~22
Code Type: X86 (Native)
Parent Process: launchd 
Date/Time: 2013-11-07 21:12:37.390 -0600
OS Version: Mac OS X 10.7.5 (11G63)
Report Version: 9
Interval Since Last Report: 199346 sec
Crashes Since Last Report: 9
Per-App Interval Since Last Report: 173 sec
Per-App Crashes Since Last Report: 9
Anonymous UUID: 5E9F31BF-2658-44E7-8ED6-A30E94180709
Crashed Thread: 0 Dispatch queue: com.apple.main-thread
Exception Type: EXC_CRASH (SIGABRT)
Exception Codes: 0x0000000000000000, 0x0000000000000000
Application Specific Information:
objc: garbage collection is OFF
terminate called throwing an exception
Can you recommend any other solutions?
Digital Rebellion has a crash analyzer
Not the cheapest thing, but a great suite of apps. There's a trial avaialble, so download and check out what's causing the crash and then post back.
Ok, so I downloaded Pro Maintenance, and ran the Crash Analyzer. It says my crashes were cause by "Corrupt Qmaster Configuration" and recommended I run Compressor Repair, which I did, and these were the results:
Detected Compressor 3.5.x.
Resetting window layout...
Checking file permissions...
/Applications/Utilities/Batch Monitor.app is not writable... attempting fix.
/Library/Application Support/Apple Qmaster is not writable... attempting fix.
/Library/Application Support/Apple Qmaster/qmasterservices.plist is not writable... attempting fix.
/Library/Application Support/Apple Qmaster/qmasterconfig is not writable... attempting fix.
Removing temporary spool data...
Checking computer name...
Attempting to start Qmaster...
Relaunching menu bar icon...
Processing complete. Errors were found during processing.
I'm wondering if somehow, whatever this Qmaster thing is was deleted or moved?