It sounds like something has become corrupted somewhere along the way. The registration information is stored in the savegame file, and your game is crashing before your new game is saved. Since you have the PPC version, there are some things that you can try before resorting to the drastic measure of completely uninstalling and reinstalling the game.

The least drastic measure is to use Explorer to locate the Plant Tycoon savegame file (in Program Files/Plant Tycoon on your Axim) and delete it. You can then try a new game and see if the problem is resolved. Also, if you have a backup of your Axim that allows you to restore single files, you can restore the file PlantSaveGame.pts from your backup to the Plant Tycoon directory on your device and see if that lets you recover your previous game in progress.

If those don't work, the only thing to do is to uninstall Plant Tycoon and reinstall it.