Why is my Hoover Pet Cyclonic belt not spinning the brush anymore?
I worked on vacuums for years, though I am not familiar with this particular model. Still, there are only a few things that can cause a roller not to spin:


roller bearings
belt
motor


The plate above the roller, or the housing above the roller must be able to be removed to get access to the belt/roller. You'll have to figure out which. There are usually plastic clips/tabs that are indicated (usually with an arrow or something). It may have a couple of screws. They should be very visible. 

Once you have access to the roller, pull it out of the housing. You may have to flex the housing to achieve this. That is ok and expected. Flexing over about 1/8" is a problem, so don't go too far. Most of the time the roller should just slide out. It probably has a lot of gunk/dust/hair around it, so you may have to finagle it out. 

The belt is usually a flat belt (though sometimes they are round). It runs from the roller to a metal post sticking out of the motor. If it is a flat belt, it will attach to the roller and motor on one side. If it is a round belt it will likely attach in the middle. 

At this point the roller should be out of the housing. See if the roller spins easily by holding the end caps. If it does not, the bearings are bad. Sometimes the ends will screw off and you can see if hair has wrapped around the bearing. If so, you may be able to remove the hair and it will function again. If not, you need a new roller. 

If the roller works, make sure the motor pulley spins. Locate the motor pulley/post. Spin by hand or run the vacuum and carefully determine that the motor pulley is spinning. If you can hear the motor, the pulley is almost definitely spinning, but not in all cases. 

If the motor spins and the roller bearings are good, all you need is a belt. Make sure you have the right belt. They will sometimes be surprisingly small. Loop the belt around the motor pulley first and then the roller, while the roller is out of the housing. Plant the non-belt end of the roller into the housing and, while holding that end in the housing with one hand, leverage the other end into the housing while stretching the belt. This can be anywhere from moderately to very difficult. Lastly, spin the roller by hand making sure the belt is not caught in the housing somewhere. This almost always happens. If you spin by hand it will naturally center out on the pulley. If you don't do this and put the vacuum back together and start the motor, it will burn through the belt very fast. 

Lastly, it sounds like you may be having some problems with the height adjustment not working correctly. I can't really tell by reading your post. If so, your father-in-law may have gotten a little overzealous with the screwdriver and taken apart part of the height adjustment linkage. Vacuums rarely need a lot taken apart to change a belt. If he went too far and you can't figure out how to get it back together, you may need to take it to a repair shop.