You don't have to be in the seat or have the park brake on to start it, although they are good ideas. The only safety switches that prevent starting are the pto switch, the hydro pedal neutral switch, and the range shift lever neutral switch. And the only pto switch is on the dash. Because this happened after being stuck, it's likely the pedal neutral switch, although it could be a coincidence and not related. The wires to the hydro pedal neutral switch or the switch itself could have been damaged when you were down in the mud. Their location under the tractor makes them vulnerable to sticks, branches, stumps, rocks, mud, etc. Make sure the pedals are returning to neutral and are not sticking. When you move the pedals out of neutral, the switch should click. Hold the key in crank position and move the pedals, and turn pto switch on and off. I have seen damaged wires, bad switch, bent switch bracket, pedal return linkage stuck or damaged, and blown fuse cause this. Also if you have a mid pto option, the lever has to be off for starting.