No reason comes to mind why a project created in 6.29 won't load in that version, whether registered or not. Try installing 6.29 on the laptop - see the link below.
As for exporting your new project with a non-licensed version: that should be possible, though certain file types may be restricted. Video AVI usually succeeds, using the default settings.
If the purchase prompt did not offer a 'lite' version choice, first save your project. Then attempt an uninstall via Windows Control Panel|PROGRAMS AND FEATURES. The choice may appear.
If still thwarted, test the free 'lite' version, which has some limitations, but should do the job for you. It may allow an Mp4 export as well. Eventually you can register it or its successor.