Do you mean Premiere ELEMENTS as discussed in this forum?
Or do you mean Premiere Pro as discussed in the http://forums.adobe.com/community/premiere forum?
Did you read the license agreement?
You are allowed to activate on 2 computers... idea is one desktop and one laptop... but not USE on 2 computers at the same time
You may also DE-activate on your old computer before installing on your new computer
In going from old to new computer, will you be staying with Windows or switching to Mac or vice versa?
Did you install from purchased download files (serial number) from Adobe or did you install from an installation disc from purchased boxed product?
Always good to give all the details along with the confirmation as per John T. Smith, are you talking about Premiere Elements 11 or Premiere Pro CS6 or other?