I tried the cold reset, and it generated the same IP address as before. I had an IT person help me with it over the phone, and it is working now. In a nutshell, you have to go into the printer's settings on the printer control panel and manually set the IP address. I will describe the process, best I can, below. But remember that everyone's IP address will be different. If nothing else, this may help people in getting into the printer settings, which is impossible to find on the HP site:
1-Take printer offline
2-Hit MENU button until you get to "MIO Menu"
3-Hit CONTINUE, scroll to CFG TCP/IP= YES (hit +/- key to change from NO to YES), hit ENTER button
4-Hit CONTINUE, scroll to IP Byte; Change to 1=192, 2=168, 3=1, 4=10 (you need to press +/- button to get to these numbers)
5-Hit CONTINUE, scroll to SM Byte; Change to 1-255, 2=255, 3=255, 4=0
6-Hit CONTINUE, scroll to LG Byte; Leave all at 1=0,2=0,3=0,4=0
7-Hit CONTINUE, scroll to GW Byte; Change to 1=192, 2=168, 3=1, 4=1
8-Hold Shift button down & hit continue
And that should do it. You can verify it by printing a new test menu.
You then, of course, need to go to your Sys Prefs > Print & Fax > Add a printer > Line Printer Daemon: Address 192.168.1.10 > Change the name to HP Laserjet 4MP (or whatever you like) > print using find the HP driver, which is in the list
And that is it! I hope this helps someone out there, and that it saves someone the time effort and money I spent on a tech call! Good luck.