It's really tricky to weed out "bad" Xbox 360's. I don't really recommend purchasing one used, since many of the early consoles had hardware issues that weren't resolved until later in the production run. Even with a warranty, I'm still suspicious. It's always possible there are intermittent issues or hardware failures that wouldn't show up in a quick test or in the first week or month of play.
However, if it's just too good a deal to pass up, I'd at least run a few tests before buying.
If you can, you might ask the current owner to sign in to Xbox Live Gold using their own account credentials. If they can get online and play a quick round of something, that's probably the best test of the console's online status.
If that's not feasible, you can probably run a quick test yourself. First, you'll need to be able to connect to the internet. Create a new profile on the box, and when prompted, sign up for Xbox Live Silver. Go into the marketplace and try to start downloading a game demo. If the console's been banned from the service, somewhere along this path, you'll likely run into an error along these lines:
In addition to testing the network and console ban status, you'll also be checking to see if the hard drive is reading properly. A more thorough test of the hard drive and the optical drive is to install a game from a disc. Microsoft's got a good knowledgebase article on the subject, including a video. The basic steps are:
- Insert the game disc into the disc drive.
- Go to Home.
- Highlight the game you want to install with your controller.
- Press Y on your controller.
- Select Install to Hard Drive.
This should spin up the disc as fast as possible, and read data continuously for 10-20 minutes. This is about the best test of the optical drive you can do in a short period.