old electric Farberware wok

I don't think there is anything wrong with the wok. Chinese wok cooking requires some seriously high heat, if it was really too hot, you'd be complaining of the oil smoking so much that your eyes sting, or even seeing the wok bottom glow if the kitchen is somewhat dim.

The more probable explanation is that, as you are not accustomed to this type of cooking, you did not know that the garlic will burn so quickly. I would suggest that you go through the options in the answer to this question about burning garlic (it's a known issue when you use high heat frying) or start with easier recipes.

So I checked the temperature of water where the element was set to about 100 degrees F. It seemed to be about 25 to 30 degrees high. So what temperature should I set it for wok cooking with garlic. I ended up cooking the dish in a regular fry pan on the stove, but I would like to use the wok, otherwise it is just dead weight in my kitchen.

Welcome! It does sound like the oil was too hot. However, in my experience with any electric fry pans, the elements don't go bad. Most of the older wok models had a plug in temperature control unit and this is most likely the culprit.

I would try your wok, perhaps with water, and use a thermometer to see if the temperature is what it is set at or how much variance you have. If there is a lot of difference in the set temperature and the actual temperature you may want to replace the heat control unit. Even though this is an older model you should be able to get one that works with it.

Last but not least, do be careful. Oil that gets too hot can be dangerous.