The Gateway computer that I've had for sometime now runs Windows
Vista, inwhich the Backup and restore has never worked properly. Just minutes after it starts to create a backup I get a message that the backup failed due to; catastrophic failure (0x8000FFFF). How can I resolve this problem?

Thanks,
Steve

In what way did you receive that error? was it a result of a blue screen (non-maskable interrupt)? If there's an error code like ones sometimes found in the blue screen I find researching the code on the net could be useful. for example, I was able to fix a laptop that was not booting properly by looking at a site that had a database of blue screen error codes providing descriptions and possible fixes. You also have resources such as the event log to see any details that could be important to know regarding the error.

An alternative I would try is maybe sticking to another more reliable back up program if the one you're using now isn't dependable.
anyways, this is a fairly old post so you might have fixed your issue by now so if you did please share how you came to fix this.

Go into the Services MMC... Check that Vista's shadow copy service is installed and not disabled.

*Disclaimer* This response is weighted by five minutes research on the stop code... I don't guarantee it works, but it makes sense given that your issue arises when performing a full backup.