For your current and new desktop license,
Read and do this before you change any parts:
https://support.microsoft.com/en-us/help/20530/windows-10-reactivating-after-hardware-change
http://www.tomshardware.com/forum/id-3164428/windows-build-1607-activation.html
Thats for the license.
Your new system really needs a clean install, rather than trying to simply migrate the OS to the new system.
There is no guarantee of it actually booting up in the new hardware.
So, you've installed a clean OS in the new PC, and transfered the license.
This leave your old PC with no license.
Your Win 7 Home license might work to activate that.
The official upgrade period ran out long ago, but supposedly it still works. Try it and see what...