FileMaker 10, 11, and 12 cannot be deactiviated. One simply uninstalls them. You can uninstall the file on the first computer and then install the software on the new computer.
From a technical aspect, if you don't uninstall from the first computer, nothing really bad happens. You can simply install on the new computer and use it there. The only thing that happens is if a use on the first computer connects to a hosted database and then you use the new computer to connect to the same hosteed database, an error message pops up and FileMaker shuts down.
Thanks for the feedback! I am in fact working off of a hosted database, so you would recommend uninstalling the program from the first computer to avoid any blockages?
Suppose I don't have a hard copy of the software, should I be able to download it with a license key from the FMP website?
IF you don't have a installer for your software, you are living very, very dangerously. What would you do if your current computer suffers a major system failure and no longer works?
You'll need to contact customer service with proof of purchase and ask them for a link from which you can download an installer. Once you have one, make multiple back up copies of it. You can put it on a flash drive, burn it on a CD or DVD, upload it to a service such as Drop Box.
There are only two reasons to uninstall the software. I am listing them, but leaving the decision up to you:
1) To stay in compliance with your license agreement. Even a single user license allows for a second install of the software so read it carefully and decide if you need to to stay legal.
2) To keep another user from accidentally locking you out of accessing the hosted database.