Playtopia requires
both Java and Flash Player. To see if they're both showing as 'enabled' click here:
http://www.test-java.com/
If one is showing as missing, go to your list of installed programs and remove it. Then RESTART your computer (IMPORTANT!) before re-installing it.
If they're both showing as 'enabled' try removing Java anyway and then RESTARTING your computer before reinstalling it. (You could also try doing the same for Flash Player but, from your post, it would seem that Java is more likely to be the cause of your problem).
Alternatively (or as well) try a different web browser!