You have not mentioned any interaction with Adobe.
Yes, you should have a valid install left.
However if it wasn't deactivated on the initial machine it may not activate on your new install.
Your only option would be to contact Adobe Support to reset the activations. Generally this has been quite painless in the past. But since the version of Dreamweaver you are using is now soon to be 4 generations back (Go Live even further and no longer in exsistance), I am not sure even they will be able to help you.
Either way your only option is to contact Adobe Support. Or purchase the latest version in either full purchase or affordable subscription method.
I had two separate "chats" with Adobe support people. I cannot find any record of these now, although they both stated that they would escalate this problem and that I would receive email. Nothing received after over ten days. I also submitted a question directly to Adobe regarding my inability to retrieve my serial number. I even attached a screen shot of the existing "About" pop-up I get on the computer when clicking on the "About" under GoLive CS.
Further insight, I am using Mac OS X 10.4 on laptop 1 and Mac OS X 10.6.8 on 2 and 3.
I expected some responses from Adobe but am so far without any. Maybe I've been submitting my requests for some assistance to the wrong places... ? Thanks for any suggestions.
I have now found the support cases I submitted to Adobe on.. "My Adobe" under "Support Case History". They are all 4 annotated with either "Closed" or "Withdrawn". I never received anything from Adobe, and have never withdrawn them. It seems I am just being marked off their To-Do list. I realize this whole thing maybe be insignificant to many, but I really need this DW program on the second computer, and don't have the funds to buy new applications right now. I'm just trying to get what seems to be a fair shake.
Nothing the user forums can help you with here.
Contact Adobe Support again. Explain your situation and ask for another activation on your CS3 install.