When the brushes on a Hoover SteamVac stop spinning, it can be caused by several things. The most frequent problem is that there is debris in the brushes such as pet hair, or lint, that prevents the brushes from spinning. Usually if you remove the brushes and clean them thoroughly, this will fix the problem. This sounds to me like what is the problem on your machine, as you make it seem as if the brushes spin, but only stop spinnning when you put them down on the carpeting.
The brushes on your Hoover are driven by a turbine brush gear assembly, not a belt. Sometimes this part can go bad, but usually when it does, the brushes won't spin at all, even when they are not on carpeting.
Anyways, here a helpful guide that I've done that shows you step by step how you can diagnosis the problem with your brushes:
First, what you'll need to do is take the brush block out of the machine. To do this there are 4 clips on the brush block. You will need to turn the machine upside down, and pull down on the brush block to where it won't pull out any farther. There are 4 clips, 2 on top, and 2 on the rear of the brushes. (See picture I have circled one of the clips in red). Simply press these clips at the same time, and pull the brush block out of the machine.
I'd say that 60% of the time that I see this problem, the main issue is that the brushes just need to be cleaned. If you have pets in the home, a lot of the time the pet hair will just be lodged inside the brushes, will prevent them from spinning. Use a pressurized water hose with spray nozzle is ideal) and spray each brush with water to dislodge any pet hair. You should be able to get these brushes spinning when you spray them. Spray each brush until the brushes are spinning pretty fast. Re-insert the brushes into the machine, and test to see if the cleaning has fixed your problem. If the cleaning still fails to fix the problem, take the brushes back out of the machine.
Now look at the brush stem that goes into the turbine inside the machine. This is the green pole pictured in middle of the brush block. Examine this pole to determine if the top of it has broken off. It should exactly how the picture shows it. Make sure that the plastic has not broken.
If the pole has broken, you will simply need to replace the brush block. If the pole is not damaged, the next thing to try is to turn the machine on while you have the brushes out. Look inside the machine, where the pole goes into the turbine (also important, make sure the switch for the brushes is turned to "Rotating Brush Speed Hi), this female receptacle should spin when the machine is turned on. It is important the try this when the foot pedal is released, and the handle down, and not in the upright position, as there is an internal switch that shuts the brushes off when the machine is in the upright position.
If you notice that the female receptacle where the brush pole is inserted is spinning, then your turbine is fine. If this part is not spinning, then most likely you will need to replace your turbine.
If you find that your turbine needs to be replaced, I have written a step by step guide that shows you each step on how to replace your brush turbine gear. Here's a link to that repair if you need to do it:
Hope this helped you, please be sure to rate my repair or leave me feedback if you found this helpful, thanks so much!