I have the same problem, except I started on an iPhone. Created a Plarium account with sole purpose of being able to continue playing my iPhone Raid progress on my laptop. It wouldn't let me because when I tried to connect them on my iPhone it said it belonged to another game or something. I opened a ticket about it and they said I needed to log-in instead of trying to connect. Now I can't log back in to my original game on iPhone with all my progress because it never asked me to create a log-in for it. So all I have is the game from my laptop which only seems to want to let me start completely over from the tutorial. With no way presently for me to log-in to the game where I have all my progress.

Long story short, don't trust the advice support gives you and be beyond excessively thorough with your questions to them about what you are trying to do before you do anything.