I would just touch the 4 solder pads with your hot soldering iron to remelt in case one cracked or came loose when you were replacing Mosfet.
Your Mosfet could be leaking current. Hard to know without seeing the circuit. Example, turning off could cut connection from battery to motor OR it may pull the gate of Mosfet to Ground.
If your new mosfet is leaking, you could measure a voltage drop across your motor or, if you clip a motor lead and connect your ammeter in series, you can see current flow. Mosfets can be damages by static while handling.