Why is my computer beeping at me?
This is unusual and should be tracked down. A malware infestation may not have an outward manifestation - you might just notice unusual charges on your credit card.
So this beep is the same as the beep on boot - the source is coming from inside the pc as opposed to the external speakers? That's indicates something is wrong.
By connecting to the internet I assume you mean running the browser. I have never noticed a beep when doing this. Try changing the home page in the browser. What browser is it - Internet Explorer, FireFox, etc.?
Do you hear this beep while Windows is booting - after bios initialization is complete?
Are all of the pc drivers up to date?
It would be useful to post the system specs including case.
"You can't use reason to talk someone out of a position they didn't use reason to arrive at." some smart guy
"Some folks believe complying with the letter of the law makes their actions ethical." MagnusTheBrewer