You could perform a basic test using joy.cpl on a Windows PC.
First, back up all the CSV files in your quadstick's flash to a folder on the PC.
Download the Default Configuration and Default Preferences files using the QMP or copy the two CSV files I have attached into your Quadstick's flash, overwriting the ones in the flash.
Then cycle power to the quadstick and follow the procedure
outlined in this article.
If things work ok, then the problem was a configuration issue. If it still malfunctions, it is something in hardware and may need to come in for service.
Since two unrelated things, the joystick and the side tube, are both malfunctioning, it may just be a configuration problem.