iOS apps not connecting/Problem logging on

I play chess on three devices: my Mac, my iPhone and my iPad. When I try logging on to my mobile apps, I get the warning, "Internet Error: Unable to connect to server. Please make sure your internet connection is working and try again." I know that my internet is working because I just refilled my data and can use every other app. When I try to access the website, it ONLY works when I use a VPN. I have exited and restarted the apps, deleted and reloaded the apps, rebooted the Mac, cleared the cache, etc. Nothing seems to work other than getting on a VPN every time to play, which I shouldn't have to do (and doesn't answer my app login issue). I running 10.9.4 on a new Mac, using a new iPad Air, and using a new iPhone 5S. Any suggestions would be helpful! Thanks.