Best thing is to install on your new machine and then try to activate it in the normal way. Most of the time it will activate because you are allowed to install PSE on two machines at any one time. However, if the activation fails, you are likely to get a chat window and you can start it and explain your situation and things will be sorted out.
Lastly, you can always re-install on your previous machine and then de-activate and this too will resolve the situation.
Good luck and post back what happened.
Uninstalling doesn't deactivate the program in PSE 9, so as far as adobe's records go you have one of your two activations already used on that computer. If you have trouble trying to install it on the new one, go here:
and you can often start a chat session right there to get things straightened out.
I took your suggestions, Barbara, and it worked!! I was finally able to get the old laptop connected to the internet, reinstalled the software, and then deactivated it. I now have it installed on my new laptop. I do have the other installation on my husband's pc, so we are both able to use it. Thanks!