I have been running 9.04 for several months, and have tried several times to install googleearth using several different methods. So far it will open to a certain stage and then trip out. Anybody got a surefire method?

It works fine here, so probably this is about graphics output or something related. Google might have better advices, but for a start you could launch it from a terminal and see if you get any (warning/error) output. Just open a terminal and run the executable (here I assume you have put it to "google-earth" directory under your home directory; if it's different from that, change the command below accordingly)
Note: if you have run it before, you probably do get a warning saying that it can't create prefs directory; this is fine.

Googleearth is available from the Medibuntu repository.

How to add the repository is shown at: https://help.ubuntu.com/community/Medibuntu

NOTE that it is a two part installation 1) Add Repository 2) Get GPG key

Refresh your sources and it should be available in your packages.