Greetings from GoVacuum,
The Hoover SteamVac's are notorious for this exact problem. There are several things that can be causing this probelm.
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 (garden 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.
One you have the brushes out of the machine, the first thing you should 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.
I hope this helps you with your problem. If not, please feel free to email me at email@example.com, and I'd be happy to walk you through the diagnosing. I also can provide you with a blown up parts schematic to your machine, please just get the model number off the back of the machine and provide, and provide me with the full model number. I do carry all parts for your machine, and would be happy to provide any technical support you need.
I tried uploading the pictures to this solution, however Fixya will not allow the pictures because they are too big. Please email me, and I'll send you the pictures.