Power Functions IR Speed Remote Control: intermittent dials

I recently acquired a bundle of Lego that included set 7939 Cargo Train, from 2010. It has sat unused for about a decade in a friend's house. There is no battery corrosion and the train motor and receiver work fine. The dials on the IR Speed Remote Control are problematic. Without even considering the train, if I turn the dials I see that for some clicks the green transmit light doesn't come on at all, sometimes it pulses briefly as expected, and sometimes it stays on for longer. This seems...