Did you completely remove the first installation? If not, remove it all to the Trash and empty the trash. Open the .dmg and copy everything to a folder in your Applications folder (or wherever). Then run the Java updater. Then run the program. DO NOT run the updater that comes with the package. My client is still saying there are new updates available, just ignore this and go into the game (hopefully!).
Appologies if this is all obvious too you, but this is usually the first step. Also, your mac isn't one of the new intel based ones is it?