I'm not sure whether that error indicates a problem with GE or with your machine, but there is another way to do it. Your places are stored in a file called "myplaces.kml", which you should find on your PC in your profile, for example:

C:\Documents and Settings\username\Application Data\Google\GoogleEarth (XP)
C:\Users\username\AppData\Roaming\Google\GoogleEarth (Vista)

So, while GE is closed, you can copy that file and paste it into the correct location on your new PC. You may need to enable the display of hidden files to see it.

If you are still having problems, please post a question in the GE Help Group.

By the way, although GE makes its own backup (myplaces.backup.kml in the same directory) it's always a good idea to save this file elsewhere, just in case of problems. Especially after any major additions!

Good luck!