Try disconnecting and reconnecting your router.

make sure you aren't streaming anything from sites like youtube, spotify, etc. You should make sure your not downloading anything while you play, ie no downloading stuff from a website or torrents. if you still can not play after making sure no other computer is doing this you might want to try checking your internet speed with something like speedtest.net (*n.b. if your wii is connecting via wifi then you  should test your computer via wifi and visa versa if it's wired) That site will let you know more or less what your upload/download is, you should make sure you test some where nearby and somehwere far away and just average them out. Should your upload/download be less than about 1 m/b then you either need to upgrade your internet plan or if you haven't noticed your itnernet going this slow your isp may actually be throttleing you (what heppened to me).