Hi,
Win10 upgrade on my Sony Vaio laptop from Windows7 had no such problem. I suspect you are troubleshooting a complex environment, and you should recall the old Computers 101 saw that says: "KISS=Keep It Stupid Simple". Troubleshooting this kind of problem is pretty near impossible on a dual-boot environment; They are notoriously unstable. When I was with dispatch while working at IBM, many of our field network engineers had up to 5 OSes including Windows multiple versions running on their laptops. They were always failing, and every time one of the OSes were update, upgraded, or messed with, sure enough, they'd have to bring their laptop into the office (most were mobile workers who telecommuted from their homes); where my tech team and I would have to resolve their problems. Our Management got tired of us spending weeks trying to recreate such multi-boot entanglements, and forbade us from doing it anymore. So, every engineer who brough in their laptop scrambled in a multi-boot debacle, was given a single OS laptop that was fully functioning. Then, if they proceeded to scramble it again with multi-boot they had their company laptop provided privelege revoked and were forced to purchase a laptop out of their own pockets in order to do their jobs!
This little anecdote may tell you why you are barking up the wrong tree with your troubleshooting methods. After 25 years in IT and 44 years in the Computer Industry you learn some things.
I recommend you wipe the drives of both your laptop and desktop (by the way, it would help to know their Makes/Models), after backing up any personal information you wish to retain from them to external media of course), and reinstall Win7 from scratch. Remove the Xeno NIC from the equation. Attempt the Win7-->Win10 upgrades on both computers using the built-in Ethernet ports or wifi (for both or just the laptop; as many newer desktops have embedded wifi now). If the built-in network adapters still fail, I suggest you have another hardware failure in one or both of those computers (RAM, Motherboard, PSU, etc.), and they will need to be fully tested; starting with the Hard Drives of both computers.
Testing your network adapters will be a lot easier if you are using single-boot configurations on each computer. So, you know until July 2016 or so, Microsoft has said that Windows10 hardware drivers including network adapter drivers are compatible with Windows8/8.1 until the Manufacturers begin changing firmware on their Motherboards to take full advantage of new advanced features in Win10. So, all you need to do is verify with Xeno that their NIC is compliant with Win8/8.1 WHQL. If it is, it should work on the upgraded desktop if you follow my suggestions. If not, it could be defective and should be returned or exchanged to them. If their NIC won't work on 8/8.1 then it won't work on Win10. Since you have skipped 3 OS versions on this upgrade, that wouldn't be too surprising. If you have access to a friend with Win8/8.1, of course you can try your NIC in that friend's computer. If it fails, that would support my hypothesis that the card is defective since it won't work on Win8/8.1, as it should if it was certified to that level. If not, or the card was only certified with Win7 drivers; you can try to exchange it with them for a newer card, or do a PXE firmware download if they offer it. Many high-performance NICs such as server NICs offer remote flash upgrade capabilities. Otherwise, have them mail one to you on their dime!!
Get back to us with your hardware specs, and let us know how it goes!
Best of luck,
<<<BIGBEARJEDI>>>
P.S. I've been doing Windows upgrades since Windows1.0 came out in 1985!
