[SOLVED] Success. It turns out that I had the wrong IP address for secure.newcorpaccounts.com. I don't know how I did it before, but I used the same IP address as secure.newcorprx.com. Anyway, I got the correct IP address, and e-prescribing in AC now works.
Craig, I did get the invalid certificate at first when I tried to go to secure.newcropaccounts.com. So I took off all internet restrictions, went to that website which loaded correctly, and that apparently got the valid certificate. Then I went back to restrict the computer, and everything continued to work as desired. So the front office computers have limited internet access, but e-prescribing in AC works... just like the doc wants.
Thank you very much to Craig for your detailed info, Indy for your insights, and others who have read about my problem.
