Here are the steps you need to follow:
1. Connect the hard disk to your PC and copy the settings.db file from G:\FreeStyle\Data\Databases to somewhere, e.g. C:\Temp
2. Make a copy to be on the safe side. If something goes wrong you can copy the copy back to the original location.
3. Download SQL Lite Browser from http://sourceforge.net/projects/sqlitebrowser/files/latest/download and install it
4. Open SQL Lite Browser and load the settings.db database from where you put it
5. Go to the second tab "Browse Data"
6. Select the GlobalSettings table from the combo box
7. Scroll all the way to the left and you will see the GlobalSettingsWeatherApiKey field
8. Copy paste your 40 characters Weather API Key instead of whatever's there
9. Save using "Write Changes" button
10. Copy the modified settings.db back to the FreeStyle hard disk, overriding the existing one in G:\FreeStyle\Data\Databases
That's all. Good luck