This definitely sounds like your belt is broken. The belt is the part that is attached to the motor at one end, and to the roller brush at the other end. If something gets vacuumed up into the brushes that prevents the brushes from spinning, the motor will continue to try to spin the belt, and the motor shaft will then burn right through the belt, or cause the belt to fall off the motor shaft, preventing the brushes from spinning. On an upright vacuum cleaner, if the brushes are not spinning, it will seem like the vacuum cleaner is not sucking well, but in fact the brushes are just not spinning.
To see if the belt is your problem, while the vacuum is plugged, in turn the machine upside down so that the brushes are facing upwards. Make sure that if your machine has a rug/ floor setting that it's set to carpet mode, and now turn the machine on. Does the brush spin? If no, then this is because the belt has either broken, or stretched out so much that it no longer can spin the brushes.
Here's a link to the owners manual for your Kenmore that will walk you through, step by step on how to to replace the belt. http://www.managemylife.com/mmh/lis_pdf/OWNM/L0403213.pdf
I have also uploaded the instruction manual to the main page on Fixya for your Kenmore 34612.
I really hope this helped you. If it did, please help other people who have this vacuum be able to find this repair on Fixya by rating the repair helpful. You may do this by clicking the 4 thumbs up icons in the right hand corner of the repair. If you have any questions about how to replace the belt, or if the belt is ok and something else is wrong, please just use the clarification request form here on Fixya, and I'll be happy to answer any follow up questions that you may have.