Hello,
Sorry to hear you are having issues. First, Start11 v1 or v2 will work great on Windows 10 OS. Second, on question will your Start11 key work on another system install. That depand on which Start11 you purchased. Did you purchase Single activation or 5 activation pack? If 5, it should work on another 4 system. But if one, than you will need to purchase another license for your second system. Do know there is discount offer to previous version owner.
Now on to your issue with Start10 on Windows 10. Try this, uninstall Start10, reboot immediately after its done. Download again, latest Start10 version from your account page. Install it, reboot again. Retest it and report back.
Thanks
Basj,
Stardock Community Assistant.