Dennis,
Do you get prompted to overwrite the existing files on the laptop when you are copying them - how are you copying them, USB memory stick?
You could try renaming the files on the laptop, then you will be able to see if you are really copying the files across.
The file you are most interested in here, is the NavData.db3 file, as this is the "source" database for all the aircraft. MyLog.db3 is just a record of what you have detected in the past, so it depends how much you need one database that has all the aircraft you have tracked.
You are restarting RB after you have copied the files to the laptop?
Ahh, just noticed that you are running Vista on the home PC - thanks Support, I missed that!