If you could provide details for what the error message says, it might be easier to help solve the issue.
Your Xbox might've somehow damaged the disc reader when it was just sitting all alone. There's a possibility that Just Cause 2's disc is too scratched up for the Xbox to read the disc. The issue most likely wouldn't be the television unless you can't connect the Xbox to the TV (which obviously isn't the case) - that would be like a computer refusing to work properly until you got a different monitor.
