Hi johnmacco,
Thanks for choosing Microsoft Community.
In your description, you're having problems with waiting for your computer to connect and not being able to print while you're printing with your HP OfficeJet 4655.
I do understand the frustration and inconvenience of not being able to use the printer at this time, and in order to help you solve the problem more accurately, we need to know some information and make a judgment based on it.
By what means is the HP OfficeJet 4655 you are using connected? Is it through a network, or a cable?
Have you confirmed the current status of the HP OfficeJet 4655?
You can check if it is currently in a properly connected state according to the instructions provided by HP.
Also, when did this problem appear? Did it appear after an update?
Or did you have this problem the first time you used this printer?
Please let me know the details above and I will provide you further assistance based on your information.
Thank you for your understanding and support and I look forward to hearing from you.
Best regards,
Zev - MSFT | Microsoft Community Support Specialist