Here are your parts
Parts for KEMS378S - AppliancePartsPros.com
Your model number is missing several characters at the end of it, so choose the correct one from the Matching Model Numbers section.

Unplug or remove power from the unit.
Remove the broil element from the unit and check the heater with a meter, should be around 30 ohms.
It is a good idea to clip something (clothespin etc.) to the wires so that they do not disappear into the back of the unit.
If it is OK then odds are that the control board is toast.

If you click on the broiler element picture in the above parts link a new page will open with more info/help on it.

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.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.

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