We recently moved into a 1997 house and I distinctly remember _NOT_ hearing any humming of any sort for a few days. Until my 4 year old banged on the doorbell a few too many times in quick succession. (I could be wrong, and the hum might have been there... but it is so loud that I would not have missed it)

Now, the basement area, specifically near the stairs is humming. When I turn off the circuit (ironically marked upstairs bedrooms), the humming stops and the doorbell stops working. Unfortunately, the previous owners (or the ones before them) had finished the basement and I see no panel/access to get to the transformer. I don't even know for sure if it is there.

Is it possible that banging the doorbell could cause the transformer to 'go bad' and start humming ? Unlikely, but just want to check

I have been reading up and found that one could use AM radios to correctly pinpoint the transformer location. Can I presume that the area where the humming is the loudest is the place where the transformer is ?
The chime is next to the door, and the humming does not seem to come from it. Unfortunately, I can't seem to pry it open without damaging it, so can't trace the wires, etc

Any help/tips will be welcome. I am really not a DIY person; but want to learn if and what I can do before forking out 125-150 bucks for an electrician to come take a look

 

That would be a code violation and needs to be changed. All line voltage connections must be in boxes that are accessible. If a friend is a doctor or nurse or mechanic borrow their stethoscope. Otherwise try a cardboard tube or rubber hose held to your air to try to localize it. A non contact tester might give you a better idea or try a stud finder with built in metal detector.

 

Welcome to the forums!

If you post a few pictures of your chime, or a link to it, we may be able to help you with that. See How To Put Pictures In Your Post.

Ray has good advice on the rest of your question.

 

First of all, all transformers hum so humming isn't an accurate indicator that the transformer is bad. That being said, I don't want to hear the transformer hum either so I'd proably replace it. Not only is it a code violation for the transformer to not be accessible, it is a worse code violation for the junction box to which it attaches to not be accessible. Once you find it and replace the transformer, I'd just install an access panel over it and leave it in the same spot.

 

I found this on ebay. This seems to be exactly what I have. Looks like the transformer is "remote" and not part of the chime enclosure.
Chinex Door Chimes Doorbell Maple Chase Company 1994 | eBay

 

A remote mounted chime transformer is probably the most common installation. What you found on Ebay is a cheapy kit containing the chime, a cheapy transformer and usually two cheapy buttons; kits like that used to sell for around $8 - $10.