First thing I would check is the power to the unit.
Remove power to the unit and check the wire nuts which attach it to power.
I would re-do them.
Then re-apply power
Check that you have 120 volts at the wire nuts.
Check that the wires up to the door switch and control board are OK.

Next I would check the door switches.

Remove power to the unit, undo one wire at the door switches, then manually activate the switch. It should go from infinite to 0 ohms.
If both are OK then it could be that for some reason they are not being activated when the door is closed.

To confirm this
You could unplug the unit, remove the wires from the switches, short them together and tape them up so they cannot short to anything.
Then restore power and give it a try.

Tape a towel over the tub opening in case it fires up.
If only way to remove power is to flip a breaker you will need 2 people as you do not want it to spray water all over and you will have to kill power quickly.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.