It is very hard to say where the problem is.
I would need the model and serial number of your unit to give exact rather general help.
They are not all the same in design.
Some had the keys on the shafts under the pulley which is what kept the pulley from spinning on the shafts.
Some, the key was actually part of the pulley and when it sheered, the pulley had to be replaced.
Some, the key was actually INSIDE the transmission (a dumb place for it).
You can not tell, but I do not like the MTD equipment at all because it just is not made well. Cub cadet used to be a fantastic brand made by International Harvestor. But, they sold their NAME to MTD and they have put the name on the same cheap equipment they sell in the Discount stores. The same has happened to Yardman, Troy bilt, Bolens, White, And several other brands. They are all the same MTD Cheap stuff now.
In speaking with my brother on the subject He had very strong feelings about it (He is also an expert here and has 37 years running one of the largest shop around).
He thinks the best idea is to sell yours on craig's list as it is and buy a New one of quality. He suggested saying that it "Needs some work, and you just did not want to invest the time fixing it" People are so Hungry to buy used ZTR's that they are overpaying for junk. HE said you could expect to get $600 to $800 out of yours without fixing it. He also considered the fact that yours is MUCH too small for your yard, and you are going to have more and more problems with it as it gets older.
He said to me, on the phone, that he thinks buying a USED ZTR is a Huge mistake (but do not tell the prospective buyer. In his experience, no one ever sells a ZTR used until after it is already causing them problems. This is not the case with regular tractors, as they many times are sold just because someone wanted a New ZTR.
He said why would you spend $3600 on a used one, when you can pay $4600 for a New one. There is a Toro ZTR commercial design that sells for that much. It is made by EXMARK who is one of the best manufacturer of commercial equipment. Toro bought them out, and has them make ZTR's for them specifically for homeowners with yards your size.
Do not get me wrong, all the Toro Front engine Tractors are the same Cheap MTD junk that everyone else sells (yes MTD has even convinced Toro / Wheelhorse to allow the name to be put on the MTD cheap junk). But, the Toro Commercial ZTR's are fantastic.
I will be glad to provide specific information as soon as I get them model and serial numbers from you, but I wanted to share this with you before we went too far.
Also, fixing your MTD ZTR is not going to add much value to it on craig's list. Weird, isn't it. Just tell them you do not know exactly what is wrong with it, You checked and the belt was was good, but someone said there might be a pin or a key sheered somewhere, you just chose not to mess with it considering it was too small for your yard anyway.