I am sorry that your Mac Book Pro is now not working on TV Anywhere due to error of device limit reached.
On your account I can see that there is one device change available. If you sign into your account, under My profile click on Device Settings. This will show the 2 devices that are registered to use TV Anywhere, you should see the Mac here. If so you can remove this from the list, then start to stream a channel and this will prompt you to register the device again.