I have for several years used the Royal Dirt Devil
"Classic" model hand-held vac for use on carpeted stairs and upholstery fabrics. Its belt-driven motorized brush makes it great at digging out the deep-down dirt.
However, it has been discontinued, I have just been told by my local vac shop person. However, it has re-emerged as the Royal Pro Series; model ER-10000.
However, I can't find it at www.royalvacuum.com, but can find it (it is now blue instead of red) at www.dirtdevil.com, for $59.95. Dirtdevil.com still shows the Classic model, also at $59.95 despite my being told it is no longer available. ???
I bought a B@D hand vac at a yard sale this summer. It is very much like the model you described. I paid a whopping buck for it. Works great and has a 30 foot cord to boot.