Google Earth won't run.

Do you have direct rendering working?
type in konsole: glxinfo | grep direct

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According to the Konsole...

root@1[~]# glxinfo | grep direct
direct rendering: Yes

As I said, I can't understand why it worked in Ubuntu, but not with MEPIS...

run it from a console and let us know what it says.

Newbie or not Newbie, there's always a question

Here is the console output:

root@1[~]# googleearth
Error: Rage 128 timed out... exiting
root@1[~]#

if you google for that error, you get some hits on different forums, but nobody has the answer yet. It also happens in Ubuntu apparently. My guess it will be a specific card and driver combination.

I don't know too much about ATI. If they offer drivers from their website, you could try installing a different version.

Newbie or not Newbie, there's always a question

i wouldn't recommend ATI drivers from their website. I've had much better results with the free drivers.

...and where would I find the FREE drivers?

I was running Ubuntu up until a week ago, and GoogleEarth worked...I don't understand what is different!

free drivers come from the usual places - the repositories.
I've tried ati's drivers on my Radeon X300SE and had worse frame rates than with software emulation. The fglrx worked better, not well enough to run planetpenguinracer full screen but enough to play properly at a smaller size.