I stumbled on this thread and thought I’d answer for future readers. You had a baseband issue. Demonstrated by going into setting - general - about and down the bottom it should have details next to modem firmware. No details means no baseband. The baseband modem connects to the network, thats why you get searching. Fixable? Yes, by a microsoldering expert. It’s a 9/10 difficulty, so you need someone with a few years experience.
This is a challenging repair. If you are a repair shop you need to quote high for it. If you are doing it for yourself, it's probably not worth the time and pain involved.
Dunno if you’re around Lee, but I’ve got a Surface Pro 3 not powering and i’d very much like to know the answer! Do you even need that sleeve?