I followed John T Smith's first link Installation Document Type (CS3 must use NEW installer and number) and arrived at this webpage: Activation or connection error when starting CS3 or Acrobat 8.
There I logged in to my account and arrived at this webpage: Obtain a new serial number | CS3, CS4. I plugged in my old serial number and got a new serial number. Under step 3 - Download replacement CS3 installer, I clicked File 1 of 2, downloaded and installed the Akamai NetSession software. I clicked file 2 of 2 but the download did not start.
Fortunately I have a copy of that download already: ADBESTDSCS3_ESD1_WWE.exe.
Following the directions on Obtain a new serial number | CS3, CS4, I uninstalled CS3 through Windows Programs and Features. Following the advice of Nancy OShea at https://forums.adobe.com/thread/1545413, I deleted the old Adobe PCD folder from Program Files (x86)/Common Files/Adobe/.
I ran ADBESTDSCS3_ESD1_WWE.exe and did not receive the message about "inserting a disk," which is the problem I wrote about initially.
I started the installation and selected all programs, then was asked to locate an AdobePDF.dll file on the "Windows Vista" disk. I am running Windows 10. I stopped the installation, uninstalled the software using Revo Uninstaller Pro, and deleted the old Adobe PCD folder from Program Files (x86)/Common Files/Adobe/. Then I restarted the installation and deselected Acrobat from the list of programs to install. Installation succeeded.
I opened up a CS3 program and entered the new serial number. Following Nancy OShea at https://forums.adobe.com/thread/1545413, I selected "Never Register." The software started up successfully.