Shoe is correct it sounds like you have your pop-up windows blocked. If you play by clicking on the "PLAY NOW" button you must allow pop-ups at least have your pop-up blocker set to allow pop-ups on WGT.
But I find it is much easier to play by using a dedicated browser just for playing WGT and only use it to play WGT. Then set that browsers start page set to the game client. That way you never have to click on the "PLAY NOW" button to play,your browser loads straight to the game client.
find a setting in your browser settings similar to this and set the start up page to the game client.