I feel like such an IDIOT. The printer has been sitting where it is for so many years with a parallel cable attached that I didn't even remember that it had a USB port in the back. Let me tell you the steps I took to get it WORKING!!
1) First off, I did what you said and moved the printer into the room with the new Windows 7 machines and hooked it up with a D shaped USB cable that I had on a USB external HD (LUCKY to even have a cable). Imagine my surprise when Windows 7 said that it automatically installed device drivers for the printer. The printer then worked GREAT as a Local Printer hooked directly to the Windows 7 machine.
2) Next, I moved the printer back into the room with the XP SP3 computers and hooked it up with the parallel cable again (I wanted to save my only D shaped USB cable for the external HD).
3) Now I tried to install the printer as a Network Printer but ran into the same exact problem as before. The computer could "see" the printer on the network but said it couldn't find a driver for it.
4) I did several hours of research on the web and hit upon a solution that WORKED!
5) I selected "Add a Printer" from the Devices and Printers menu.
6) I selected "Add a LOCAL printer"
7) In the next menu I selected "Create a new port" and "Local port"
8) In the next menu where it asks "Enter a port name", I entered \\DELL8100\970Cse
. ("DELL8100" is the name of the computer that shares the printer and "970Cse" is the name of the printer share) In my humble opinion the "Enter a port name" should be labeled "Enter a port PATH" instead!!!!!
9) Then I just kept hitting "Enter" until it finished.
Imagine my complete and total surprise when I selected "Print a Test page" and I could hear the old HP Deskjet 970 Cse printer come to life in the next room. I AM ELATED....
Your advice about hooking the printer directly to the new Windows 7 machine first in order to automatically download drivers worked GREAT. To be honest with you, I don't know whether or not the whole setting it up as a local printer through a new Local port would have worked or not if I hadn't followed your advice and gotten the drivers through Windows 7 directly.
In any case IT IS WORKING and I owe you a debt of gratitude. I also added to your reputation (I think) by clicking on the button. THANKS AGAIN VERY MUCH!