Performing an unsafe shutdown of any OS is a bad idea - it could easily cause data loss including file system corruption to the point where the OS may not boot successfully afterwards.
It is unlikely that Linux is affecting the router at all really. It is most likely that it is putting the network adapter in the PC into some sort of low-power state that Windows doesn't know how to wake it up from. The first thing to try is making sure that Windows has the latest driver for the network card in your machine.
Also, try completely powering off the PC (and by "completely" powering off I mean flip the switch on the PSU or wall-socket) between shutting down Linux and starting Windows, which should fully reset the network adapter (unless it remembers the state in non-volatile memory so the condition survives a power-cycle). If this has the desired effect, while far from ideal, it will save you needed unsafe shutdowns until you have found the cause of the issue.
Another option would be to try another network card if you have a spare one handy. If the problem goes away with another NIC that will prove the problem lies in the old NIC or the drivers for it.