@Fine_feather
Thanks for reaching out to us on HP Support Forums. 🙂 I came across your post and would like to help.
I understand that you have an HP Deskjet F4580 All-in-One Printer and post upgrading to Win10, the printer does not print wirelessly. The printer prints fine over USB and also the printer prints wireless from your wife's laptop. I appreciate the steps you have performed and have certainly done a good job.
I suggest you to perform the USB over wireless setup to connect the printer wirelessly to your computer. Please click on this link. NOTE: Follow the steps mentioned under Windows 8. These steps are compatible with Windows 10.
Feel free to let me know the outcome. I'm always here to assist. Cheers! 🙂