I recommend against that...
Assuming the last backup was performed before these problems began, I would not delete it as you may need to use it in order to resolve the current issue without reformatting and starting over. Even in the best case, it's a backup of your files you should not surrender until you have another recent backup of those files.
Since HP's maintenance program identified file corruption, I would start by running System File Checker per these instructions. You'll want to have your Windows 7 DVD ready in case it is requested. In addition, I would verify that the external hard drive has sufficient room for another full backup and try using a different backup media to see if it is the utility or the hard drive that is the issue.
Note: This post was edited by forum moderator to correct broken link on 10/29/2010 on 2:32 PM PT