If you have received the error code 3151-0000-0080-0300-8007-2751 while attempting to update or download on the Xbox 360, this is likely caused by a corrupted profile.
The problem generally causes the Xbox to abort the download, and sometimes the console will drop the connection to the router, which may give the impression that the wireless adapter attached to the Xbox is faulty.
However, for this specific error, an Xbox networking or connection issue is likely not the problem, and you can save yourself a good amount of troubleshooting time by trying this solution first.
Correcting the Error
First, check your Xbox network account status. Look for expired credit cards or other problems that might be causing an error.
Next, delete the bad profile. This error is generally caused by a corrupt profile, and the solution is straightforward and should correct the issue.
Though the problem that results in this error is likely a corrupt profile that can be solved by deleting it, the error code is part of a group of errors that fall under the networking error family, so there may be other issues involved if deleting the bad profile doesn't solve the problem.
Try these solutions if you are still having issues.
Clear the Xbox hard drive cache. From the Dashboard, go to the System menu, select Memory and then Hard Drive. Press the Y button and choose Clear Cache.
Clear failed updates from the cache. Turn off the Xbox 360. While holding the Sync button next to the memory unit slots, turn on the Xbox. This will clear the download queue and restart failed downloads.
Check that the problem is not on your router. If you use a router, bypass it by disconnecting your Xbox from the router and connecting it directly to your modem. Attempt to update and see if it completes successfully. If it does, reconnect to your router. You may need to check your router and its settings.