I'm asking, because you did not specify that you are using the same cable on the PC that you use in the car. If it was me, I'd have one cable in the car and one cable connected to the PC, so that I'm not constantly plugging and unplugging it and wearing out either the USB port or the USB connector on the cable. I'm trying to confirm you ruled out the most likely cause (bad or worn out cable).
If you have not already, do a Reset (restart) on the iPod, and then try it again.
Learn how to reset your iPod - Apple Support
If that does not help, you may want to do a Restore on the iPod using iTunes. It's not that likely, but there may be data corruption on the iPod affecting its software. There has not been any software update for your iPod in a long time, so it's not a recently introduced "bug." The Restore erases the iPod, reinstalls its software, and sets it to default settings. The Restore button is on the iPod's Summary settings screen in iTunes.
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If that does not help either... If the cable is fine, and the iPod works when connected to the computer using the same cable, the cause is likely to be a problem on the Pioneer system or at the connection point to it. I know you said that other device works, but it uses a different cable to connect. It sounds like you are connecting and disconnecting on that USB port often, so it may be worn out in a way that no longer makes a data connection to the iPod's USB docking cable (which is probably worn out in a similar way). That other device's cable may have less wear on its connector, so it still connects. And your computer's USB port may be fine, so it still connects iPod using the same cable.
If you have or can get a new (or newer) USB to 30-pin docking cable, that may allow you to connect the iPod to the Pioneer system. And if that works, you may want to leave that cable connected most of the time, and use the existing one with your PC only.