My second Dreamcast controller stopped working. Comparing it against a known-good pad, the problem looked obvious: the pins on the cable’s connector end were pushed in.

While looking into it, I came across a Dreamcast controller restoration video that pointed toward the fix — rather than trying to coax the damaged pins back into shape, or opening up the controller to re-terminate the wire, the whole cable is a cheap, easy swap. Replacement Dreamcast controller cords turn up for a few dollars on AliExpress, or a bit more on eBay.
I picked one up, and the fix was as simple as it sounds: no soldering, no disassembly beyond opening the shell to swap the connector — just plug and play. Fixed.
If you’ve got a Dreamcast controller with the same pushed-in-pins symptom, this is worth trying before anything more drastic.