Again, thank you for a clear and simple guidance for a non-tech person; some of what seems very obvious to experts is not in the obvious understanding of those of us less-steeped in computer 'know-how', thus we are grateful for your knowledge and patience.
So, having linked onto the instruction manual and pushed both WPS buttons (router and on printer through HP instructions and printer happily indicating it is online and desktop indicating that printer is selected), I tried to print again and printer still saying that it is 'offline'.
My apologies as I cannot seem to get this connection sorted. Any further suggestions? It is very frustrating as you can appreciate.
Ok, having tried the WPS buttons and had no joy first time around, I did it again and then went to re-install printer as wireless (transfer to wireless) through USB. The same messages appeared: 'printer rediscovery problem - may not track online status changes of printer'; happened just as installation was almost finished and message said checking status of SLP for IP address. No joy, then asked to check Firewall UDP ports (same as last time) were unblocked and then to check turning printer on and off. I did not do the Firewall thing again but tried printer on and off. Hit 'retry' and this time printer connected through wireless said successfull, unhooked USB cable and printed test. Then printed own doc, first came up as 'save' only but changed device to printer and it worked. Has done docs from other sources so seems to be working.
Sorry, really don't know what happened and cannot explain it for future people with the same issue, but happy that it is working for the moment.
Thank you for all the help and advice - good luck to all the others with this printer problem after conversion to Infinity!