I believe many Linux distros are missing drivers for the Broadcom WiFi adapter that comes in the Mini 10v. Depending on the distro, it can be easy or awkward to install the drivers. I dunno about Puppy Linux.
In Windows, you may have to install drivers, too. Plug in via a wire to get the drivers, Windows probably has a driver for the wired connection.
If installing the drivers doesn't help, test by running "sudo lspci" in a Linux terminal. That'll list all PCI devices, even those without drivers. Your network card should be among those, unless there's a hardware problem or it's disabled in BIOS. You can perform a similar test in Windows by looking in Device Manager for devices with exclamation points.