If you have a multimeter, check the wiring on the connector cable to be sure that there is electrical conductance through each wire in the connector cord.
If the connector cable passes the test, then the issue is with the joystick or PCB. Check to see that all the wires are properly soldered/connected to the microswitches. Do conductivity tests with their lines, too. You may have to take the joystick completely apart to see if there’s an issue with the pivot, the spring retainer, or actuator. Pop off the E-ring retainer to see if the parts are okay. If that stuff checks out – no broken pieces of plastic or spring issues causing the joystick’s bad behavior, then something on the PCB is broken or worn out. IF your stick is broken – worn microswitches or other issues --, you’ll have to mod existing in-production parts to fit OR figure out a way to fit a small replacement stick into that cramped base. JLF’s and LS-32’s will definitely NOT fit into the SS case. The microswitches should be easy enough to replace… Just find similar construction switches from Sanwa (JLW series) or Seimitsu (no -01’s).
Sounds like your problems are a little bit of both the connector cable – it shouldn’t be malfunctioning like this at all – and the joystick. Possibly the PCB is broken some way. Don’t know what to tell you if none of this checks out negatively other than that the Hori PCB may be shot. In that case, you have to ask yourself whether the stick is worth saving for a mod. The case is very shallow as it is and it would be hard to fit anything larger than a Cthulu-series PCB in it let alone a dual mod with a 360 PCB.
For what these SS sticks generally go for now, I would say get another joystick. SS mods are involved and not much in-production hardware can be fit into the cramped case space without some plastic cutting.
There are definitely some people who might buy the case off you. At least you can recover some money there. Those guys use it as a Neo Geo stick stand-in after some serious modding…
I had one of these SS sticks, too, and never felt it was a comfortable stick. I always felt the Ascii Saturn stick had far more comfortable buttons although that stick base is even less moddable than the Hori SS Stick. At least with the Hori SS Stick you have the ability to fit in quality 30mm buttons if you just widen the existing button holes a bit – not that I seriously think it’s worth the effort.