With nothing other than picturing how the mechanism works and is set up, it SOUNDS like the internal mechanism that actuated to reset the trip odometer has, for lack of better term, a 'closed' position where the trip odometer logs mileage, and, an 'open' position that occurs when the shaft/button are pushed in and turned.
If the mechanism became stuck into 'open' the trip odometer would set to zero, but, remain in an interrupted mode where new mileage couldn't be logged.
I've never taken one all the way apart, but, if the knob worked by a prong on the 'toothpick' as you've dubbed it rotating and them either pushing open, or on, some tab or other part to trigger the reset, and, either than prong, bump, whatever you want to call it, came off to hold things in the 'open' position, or, it was turned a bit too aggressively by someone and bent/forced whatever it triggers internally to become 'open' for reset purposes and can't spring back to 'closed', it would lead to the symptoms described.
Just brainstorming here