I'm struggling to follow your post but I'll try to offer assistance:
>>>I click on google internet
Er, no you don't! (Well, not exactly, anyway!). Assuming that your computer is connected to a router (either via an Ethernet cable or wirelessly) it's connected to the internet as soon as you turn it on and (for example) it will automatically check that your anti-virus software is up to date before you've clicked on anything.
If you want to browse the world wide web, the next stage is to open a web browser. The one that comes with Windows is Internet Explorer but you can use any other browser, such as Firefox (which I prefer) or Chrome. Any of those browsers can be used to access Google's search engine (although Chrome is actually made by the people behind Google). So I haven't got a clue as to what you're referring to when you 'click on google internet'!
Further, it's not clear what happens when you 'go off and then try to get Google again'. If you simply walk away from your computer there's no reason why your browser shouldn't remain open, enabling you to continue using it as soon as you return. (i.e. there should be no need to click on anything at all).
My own preference would be to forget about whichever browser you're currently using and to install to Firefox (which allows you to search Google from the box at the top right, if that's what you're seeking to do):
https://www.mozilla.org/en-GB/firefox/new/
That should work as I've suggested, i.e. by simply remaining open, and available for use, when you leave your computer.
However I think that we might need clearer information if we're to get to the real cause of your problem. e.g. exactly what is it that you actually click on and what happens if you leave your computer for a while. (Does it simply freeze or totally close?)