I had a TSA approved SwissGear 3-combo luggage lock (not build in to suitcase/bag). When I got it back from TSA at one point, the lock was jammed, but not fully locked it seemed. When I did manage to pry it open, it was thereafter stuck in the open position.
To get into mine, I tried everything I found online (such as slowly turning 1 dial at a time while listening for any change in "click"), but ultimately managed to do it by observing the dials themselves when I applied pressure. So, I simply pushed down on the lock/latch, and observed the first dial (closest to insertion of lock shaft). It seemed to turn slightly whenever I applied pressure, indicating that the lock shaft was not seamlessly sliding past that dial. So, I turned the dial 1 click to the next number, and observed again; same thing. I repeated this until no observable movement occurred, and then repeated the whole process again for dials 2 and 3, serially (with the 1st dial still on the number I assumed to be appropriate based on "testing" it via this above method).
In this way, I eventually managed to close my lock and I reset the combo back to my original using the code I had found out in the above manner. Turns out my code was changed in full by TSA somehow - none of my numbers were the same. Just glad I figured it out somehow.