There is a system of gears, rackets, and paws in the wheels. Dirt and grass get in these and jam them or damage them. The wheels will need to be taken apart checked and cleaned and any damaged parts replaced. At least yours did at one time have a free wheel reverse mode, I would say at least half of the S/P mowers on the market DO NOT have a free wheel reverse mode at all. I say you should take it to some one who knows Husky S/P mowers because some of these wheel rackets systems can be a bit tricky to work on. As to cost it is hard to say.
"DEFECTIVE OWNER/OPERATOR NOT COVERED UNDER WARRANTY"