Hello doreron,
Welcome to the Forums!
I am sorry to hear that your Deskjet F4580 is showing offline on your Windows 8 laptop. I have looked for some information for you on this issue and have found a troubleshooting guide that I recommend for you.
Please see the guide below for the instructions. I hope this helps!
'Printer is offline' Message Displays on the Computer and the Printer Will Not Print
All the best,