Both of these are by Jeff Lynne (of ELO fame), from the hard to find but much loved 1984 movie Electric Dreams. (Which just this year finally came out on DVD for the very first time... for Region 2/PAL only. )
I never knew "Video" had an official video, but thanks to the Youtube, here it is. (The bearded sound effects engineer in the video is apparently played by Bud Cort, who was the voice of the computer in Electric Dreams. And yes, that's a young Virginia Madsen in only her second film role.)
"Let It Run" never had an official video, as far as I can tell--which is unfortunate, because it's such a fun song--but this Xena fanvid almost makes up for it. (And I generally don't go in for fanvids.) Warning, plaid crack ahead!
Let It Run's original movie sequence is almost as crack-tastic in its own way, and well worth the watch. ("That's tellin' 'im, Howard!")
Feudalism: Serf & Turf