Can't connect or sync iPod mini

We gave our kids our old iPod minis. They work fine and are still in great condition. Not sure when we last synced them, but they will not connect to any Windows desktop or Mac laptop in our house. I switched out the cable, reinstalled iTunes, tried accessing it from the device manager...pretty much everything on the various other posts suggested.

I don't know how to turn off the iPod nor put it in recovery mode.