Your external drive must me USB 3 Try the below by finding the files and putting them on a USB 2 flash drive.
You need to load the USB 3 Host Controller and Hub drivers at the beginning of the restore process. Then the reimage software should see the disk and image. With Windows imaging you go to the load driver option and select the 2 appropriate *.inf files.
Boot from the Windows 8 DVD and try restoring your system.
Since Windows 8 is three years newer than Windows 7, the drivers loaded at boot time should include those necessary to handle your USB3 external disk.
DISCLAIMER: I HAVE NOT TESTED THIS IDEA! I AM ONLY SPECULATING!
Cheers, PW.
P.S. Those who did not get a Windows DVD with their computer may wish to download a Windows 8 Evaluation .ISO and burn a disk. Even if Windows 8 is never tried, the disk still has the code needed to repair systems that are unable to boot.
And if they want Windows 7 (SP1) .ISO files, use these links. . .