Barb, FWIW I had the same thing with end of the world sound effects when I jammed a dado at close to 3/4" into a new insert.. Mine didn't stop the saw, but it scared the beegeejeepers out of me. I powered mine down due to the racket. My thought is sawing out a single blade insert like you have to, by coming up through the bottom. Add to that noise, several blades, and all of those extra teeth, and it just adds a din that sounds like it's the end of the world. Did you look at the bottom of the insert, and did it looked pretty chewed up? It doesn't get smooth, until you exit the insert. Probably a lot of noise, and enough stopping force to quit your motor. Are you direct drive, something with a belt. like a contractor saw, or a cab saw with possibly a few drive belts?
If you feel it jammed on something inside the saw, probably best to post make and model, so maybe someone with same/similar saw could weigh in, and hopefully make you feel better about potential, but I really doubt either a 1/4" or 3/8" dado would strike anything on any of the brands I am familiar with, but if it is a smaller direct drive saw, I know almost nothing about them, nor the clearances they have. I do know on a few of them, I have read they do not accept a dado blade, but I couldn't remember which they were, with exception of that little Sawstop. Beside them, most saws these days allow for a 13/16 dado, and have appropriate clearances to make that happen.