Guess it depends on what you consider "elderly" ;) If you go back more than a few years, Basecamp was really rough around the edges. You might be better off with Mapsource, Garmin's older software that is no longer supported but still available. You can download older versions of both programs here. With Basecamp, you might have to just backtrack until you find a version that will run on your machine: http://gawisp.com/perry/mapsource/
If you want to use Garmin's newer maps, you will need Mapsource version 6.14.1 or newer. With Basecamp, I think you need version 2.08 or newer. There is a way to convert the new format maps to the old format if needed however. http://www.javawa.nl/cne2009_multilang.html
You can also use free third party maps, such as Openstreetmap, TalkyToaster or GPSFileDepot. These typically will work on older versions of Mapsource/Basecamp.
I'll let someone else explain the Google Maps part. It should certainly be possible, but I don't use Google maps very often.