After trying several remedies, the following finally worked:
I had to delete all of my adobe products from the computer (Photoshop, Acrobat, etc). Not just Dreamweaver
Then I used the "Creative Cloud Cleaner tool" I found on these forums (I choose "all" for the cleaning choices)
Use the Creative Cloud Cleaner Tool to solve installation problems
Then I cleared my cache
Then I went into programs files and deleted anything that remained with "Adobe" on it
Restarted my computer
Then I logged into this link and got my new serial number https://helpx.adobe.com/creative-suite/kb/activation-fails-cs3-acrobat-8.html
Activation or connection error when starting CS3 or Acrobat 8
I then used the link from the above page to download a new version of Dreamweaver CS3
This time it asked for the new serial number and it was accepted.
I then choose "never register" when promted
And I was able to use my program again.