Our microwave now does a constant humming noise when it is plugged into power.

If your microwave is making an unusual or loud humming noise, you may have a problem with the magnetron. This component is part of the high voltage circuit and provides the microwaves that generate the heat. If the magnetron is defective, it may cause a loud humming or buzzing noise.
https://www.fix.com/repair/appliance/microwave/unusual-noise/

It could be the possibility of the bulb about to go out or dust in the fan

follow this steps and use the VOM , and fix it. God bless you

1. MagnetronIf your microwave is emanating high pitched or growling noises during operation, the magnetron could be going bad. Normally a nearly silent part, the magnetron uses high voltage and induces the frequency required to cook food. Although normally not a safety hazard to operate, this is a sign that the magnetron is failing and will need to be replaced as soon as possible.
   
2. Exhaust fan motorIf your microwave is making a very loud humming noise during operation, it could possibly be the exhaust fan motor. If defective the part will need to be replaced to silence the appliance once more.
   
3. Stirrer motorAnother leading cause of a noisy microwave is an expired stirrer motor. With use this part becomes worn and makes a loud grinding noise, which is usually a leading indicator that the part needs to be replaced. The stirrer is a metal blade that is slowly turned by the motor. This action disperses the microwave energy in a random pattern, which heats the food evenly. If the stirrer motor is determined to be nearing expiration, it should be replaced to halt the grinding noise.
   
4. Turntable motorA very common cause for a noisy microwave is a worn out turntable motor. This is a relatively easy repair and will put an end to the noise once replaced.
   

This is the power transformer humming, sometimes when transformers get older you get vibrations in the windings due to magnetic fields generated within the transformer which causes the humming noise, It's more annoying than anything and won't affect the operation of the microwave.

May as well use the microwave as is until it terminates naturally. All microwave ovens buzz, that nothing unusual, but although you can replace a Magnetron, the cost is unusually high. By the time you take the oven down, open the case and fuss around, perhaps not making things any better; the fact is; a new replacement with a warranty is just over $100. Why bother?

hi it could be a bad neutral connection on your plug or inside on your high voltage transformer check the plug for burning and try plugging it in a different socket

Hi,
Here is a tip that will help you to figure out what is wrong with your Microwave Oven....

Basic Microwave Oven Troubleshooting Tips

heatman101

The constant humming noise you hear when the microwave is plugged-in but not running is caused by the Low Voltage Transformer, which is located inside the back wall of the outer cabinet on the left side. If the microwave is working properly otherwise, there is no hazard, just the annoying noise.

To access the transformer, the microwave must be taken down and the outer cover removed. The transformer is held to the back wall of the cabinet with four screws, and there are two sets of leads with pull-apart connectors. The noise is the result of 60hz vibration being transmitted to the sheet metal from the transformer which may not have been sufficiently "potted" or otherwise mechanically isolated when manufactured. You can either replace the transformer or try wedging some thin rubber or other material between the transformer and the sheet metal to quiet the noise. Just be careful to not damage the windings!

Often over the years the Transformer laminations can loosen, from the on/off rising and collapsing magnetic fields, and then they sorta hum louder. I suspect this is what is going on. Shouldn't be too much of a worry.. keep an eye on it tho.

the most common problem with ALL microwaves is the magnatron