Hmmm,

when I am online my computer is receiving data constantly even when I don't have a browser open.
That is what you should expect. You make a connection to your Internet Service Provider. Your PC and their server remain in constant communication to check that the link is still working and for the server to follow your instructions.

If something goes wrong, and the connection is lost, your PC will pop up a message about it.

What is happening in the example you have given, is that your system is trying to contact Google. That may be your service provider's default?

I don't know what your startup settings are, but try putting your homepage into bookmarks/favourites and setting your homepage to blank.

See what happens then, particularly, does anything try to reset your start page in your browser.