Well the easiest way is to copy the whole Palace folder onto a memory stick or burn it on CD, then copy it to the program files folder on your new Windows computers.
The advantage of Palace is that you don't have to actually use the installler to run it.
If you are moving to Windows Vista, check out the vista fix:
Palace Planet the Palace Chat community Portal - Vista registration code work around
When you copy the entire Palace folder your client will not be registered because the registration code is not inside the Palace folder:
To keep your registration code the same, you need to copy the Palace.reg file from your old Windows folder (C:/windows/) to the new Windows folder, this might be tricky if using Vista, I think Vista hides its Windows folder.
Or if you have it, use the old registration code to register the client the old fashioned way from the registration menu in the Palace client.
If all goes well you can run your Palace the same way you always have done.
By the way you do not need to copy the media folder, if it is to large you can leave it and re-download all the media.
good luck.