Hi,
Perhaps the replacement belt was of the wrong diameter or thickness.
Here’s a [https://www.petervis.com/walkmans/sony-wm-4/sony-wm-4-drive-belts.html|link] that describes the specifications for the 2 drive belts used in a Sony Walkman WM-4
Here’s a link to just one [https://www.ebay.com/itm/NEW-Replacement-BELT-SONY-WALKMAN-WM-4-WM4-Cassette-Player-/152814804570|supplier] of the belts. It is only shown to give you an idea of the cost of the replacement belts. There are other suppliers online that may suit you better.
As for the Stop button, check on places like Ebay etc for a faulty Walkman WM-4 that you can salvage the button from. You may be lucky that someone is trying to sell a faulty unit at a price that suits you