So to summarize, for the Windows 8 computer, NONE of your iPods react (as indicated by the iPod's screen) when you connect the iPod? And on the Windows XP computer, the two 5th gen iPod nanos "work perfectly," and the 7th gen "ipod screen says Connected and Eject before disconnecting" (although it does not appear in iTunes).
If that's correct, I think the Windows XP computer and its iTunes installation are working properly. IF the 7th gen iPod nano is the the 2015 version, it does not work with Windows XP (and the last version of iTunes for Windows XP), so it makes sense that it connects but it does not appear in iTunes. And the older 5th gen iPod nanos work fine.
But your Windows 8 computer is not connecting at all to your iPods, not even for power. It acts like you are not connecting them to USB. Even if iTunes is not installed, the iPods should be seen as unidentified USB devices. At the very least, the iPods should show battery charging symbol. Have you confirmed that the USB ports are working properly on that computer, by connecting something else to them? Connect something that is data-related and uses power from the port, like a USB flash drive.
Since it's a laptop, it should have its power adapter connected, so that it's not running on battery power. The laptop (and Windows 8) may have functionality that turns OFF full power to USB ports when running on battery power, to conserve power. Without full USB power, the iPod may not connect or charge its battery.