I believe the Trial version registration code is for one-time only and time-limited use. Since you have previously had the software installed, registered and running on another machine I don't think you can use that same number to activate it on your new install.
However, you refer to Independence Free; I don't believe the Free version requires a serial/registration key so are you sure you are not running either of the paid-for versions, Pro Standard or Pro Premium? They do require a valid key.