The restore should proceed no matter what PC created the backup. Is the backup on CD/DVD, and external disk or a network Share? Is the restore happening via the same path? That means, if the backup was made to an external disk connected to computer A, is that disk now connected to computer B or are you connecting to it over the network for the restore, as an example.
Since the error is less than helpful, I recommend that you contact support:
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
-steve