If the service is running but nothing updates, then I'd start looking at firewall or IP address issues. Did you check to see if your computer's IP address is the same as the old PC? You may have to update the proxy address in the GW. Make sure you use a static IP on your SkySpy box and use that address in the GW proxy setting.
I don't have a Win10 box - it's a bit early for that just yet, since it is still in beta. Let me know how things go.
There are some rumors going around that Win10 is simply a M$ trick to get all Windows users to buy in to a subscription based operating system. You get Win10 for free the first time, but you have to agree to automatic updates. Then comes the monthly subscription - buy it or your updates quit. It could also come to pass that your OS moves mostly to the Cloud. In that case, its pay or say goodbye to all your files.
I would not be comfortable with a forced-update business model for Windows, or one where I have to remote in to my Cloud session. What happens when the dump "Vista2020" or "Son of Win8.0" in our laps during a nightly update - a real stinker, especially when the previous OS version ran just fine.