Serial numbers are coded for the date of factory production, nothing else useful. Model number is needed to identify the machine's mechanical specifics and service information.

Kenmore elite series SM9710803-A is that the correct one?

Kenmore appliance model numbers are typically digits in the format xxx.xxxxxxxx. Find it on the model/serial tag which is/should be affixed somewhere around the loading port and visible when the door is open. The first three digits (before the period) is a code for the source manufacturer (Sears/Kenmore doesn't itself manufacture anything). Elite is a marketing name, not relevant to the model number. The format of the serial number you cited looks to be Whirlpool, so the model should begin with 110.

Tripping a circuit breaker is of course an electrical overload problem. Testing is required to identify the source. Could be a bad/shorted motor control board, motor itself bad, pump, or some other component. Maybe the breaker is bad, weak.

Humming/buzzing then tripping circuit breaker is usually, as dadoes mentioned, caused by a stalled or seized motor or pump which could be caused by a small piece of garment like a sock stuck inside the pump. Sometimes you can detach the drain hose from the pump (put some kind of pan underneath to collect any water that will leak out) and look inside for any foreign object, and if that's the case, you can remove it using long needlenose pliers or something alike.

Please under no circumstances put your fingers or any part of your body inside the pump. If it is blocked by a sock or other object it might kick back when your remove it and you could be injured.

I doubt your circuit breaker is bad.

So the model number for the washer is, 11020942992. I also checked the drain pump lines and nothing, it was all clear.

Washer fills with water but as soon as it goes to spin or agitate then it shuts off and breaker trips.

This is Whirlpool-built direct-drive mechanism. The pump is mechanical, not electric, so it can't be the source of the problem. The drive motor may be shorted, or a wire is shorted, or a problem with the timer or the speed selector switch, or some other electrical component such as the motor's centrifugal start switch or capacitor. You'll need to investigate, diagnose the source of it. Or call a servicer if that's beyond your DIY skills. Do you know how to get access to the motor and wiring?

If you feel comfortable taking the machine apart, you can first unplug the machine and see if you can spin the motor shaft by hand (from what I can see on the parts diagram you will have to remove the pump to gain access to the shaft). The motor shaft should turn easily by hand. If it is seized, either something is wrong with the transmission or the motor's bearings are seized.

If the motor turns easily, it is probably an electrical problem like the ones listed by dadoes. I would take a chance replacing the capacitor. Be careful while removing the old capacitor as it can hold a charge of up to 120 volts even with the machine unplugged. Make note of which wire goes where, and remove the old one and read the specs from it. Specs will read something like 350-385 mfd 120 vac. You can go higher on the voltage, but the important value is the mfd. It must be within 10-20% of the value of the old part.

A jammed pump could cause the motor to not run, since the pump is mounted directly to the front of the dual-shaft motor. But that would normally cause the motor to kick-out on its internal overheat protector (which auto-resets when it cools) and shouldn't (normally) cause the circuit breaker to trip.

So would it solve the issue if I just replace the whole motor for the washer? Or would my issue be from something else

It's important to identify the source of the problem instead of blindly changing parts that may not be involved. That's known as a PCM (parts-changing monkey) in the service industry.