I know this is not fuzzy-warm, but it’s possible your system failed because Skype wanted it that way. Skype got to be the ultra-reliable chat application by viciously and unpredictably taking over your computer’s sound services. It’s not unusual when Skype rejiggers settings for far-side recording to drop dead. Local recording is handled through Windows, but far-side is handled through Skype services.
Audacity is not recommended for recording Skype.
You might like Pamela or one of the other Skype recording applications.
http://www.pamela.biz/en/products/
https://forum.audacityteam.org/t/help-recording-with-a-mic-laptop-and-headphones/35068/6
Others may be available since we wrote that. Post back if you find one you like.
Koz