How can I find out what the firewall issue is on a Printer?

I was having problems reinstalling HP software for my All-In-One printer,
and HP Tech support had me add ten or fifteen programs to the Firewall as
allowed programs, plus about that many ports. I'm still having firewall
issues according to the HP networks diagnostic tool, and the HP software
does not "see" my printer on the network.
I can go to its IP address in Internet Explorer and see info about its
status, etc, and I can install basic drivers for other similar printers and
it will print, but not from the Full Software package that I need for OCR
scanning. It is listed under Printers and I can print a test page.
The HP Diagnostics has a AutoFix button but it doesn't fix the issue, and
doesn't say what is wrong. Until I had problem reinstalling the software it
had worked fine for two years.
How can I find out what the firewall issue is?