I'm going to assume that you never upgraded to WeatherCat 2. In that case, you can use the current version for 14 days and then will have to pay the fee to continue. Alternatively, older versions are available on the Trixology website and you could download and run an unsupported version with your version 1 license.
Now if I'm wrong and you already purchased a version 2 license, just input the info into WeatherCat on your new computer.