Carburetor probably needs removed and cleaned and while at it check and replace if necessary fuel lines also check fuel tank for trash and clean if necessary.
ALWAYS disconnect the battery to frame (ground) connection while servicing electrical systems.
There should be two larger red wires (~8AWG), a smaller red wire and a smaller Orange/White wire. Identify the large red wire from the starter and attach it to either of the two large solenoid contactor posts. Then connect the other large red wire comming from the battery AND the smaller red wire to the other large contactor post. Then connect the Org/Wht wire to the smaller solenoid (+coil) post. Reconnect battery ground.
Refer to wiring schematic
https://www.partstree.com/parts/mtd/mowers-lawn-garden-tractor/13bc76lf058-murray-lawn-tractor-2014/wiring-schematic-725-04849c/
Check both rear wheel have their square drive keys in place, if either wheel has been removed for some reason it is easy to refit the wheel without the key in place, the drive shafts will then just rotate within the centre of the wheel.
many places like agway, true value hardware sell misc pulleys. you can bring in your bad one and size up the new one.
Maybe "repairclinic.com OR eparts.com can help