GE T34FS When one pushes
The release mechanism is going to be exactly the cause of the problem. A steel plate, attached to the inside plastic handle, engages and is held by an electromagnet as the handle's pushed down. When there are any crumbs obstructing the plate from good contact, the transformer's current varies, trying to bring the contact to the electromagnet's plate. This causes the transformer to hum, or buzz. The fix is to clean it out, and sometimes you can hold it upside down and shake it out. Otherwise, you will have to disassemble it and clean it out.
After that, it should work like new.
One other thing to check, is that the transformer is tightly secured to the circuit board. If it works loose, it will vibrate and cause noise.
Last suspect component would be a failing capacitor or component in the circuit board breaking partly down, which takes an oscilloscope to pinpoint, in which case it's cheaper just to buy a new toaster.
Good luck, thanks for using FixYa, and hope this helps!