Look in Control Panel > Network and sharing center for the "View active networks". If there's nothing there then you're not connected.
Or hover over the network icon in the system tray and see what it says.
Or try to open a page in the browser, and if you can - it's connected, if you can't - it's not (unless a firewall is in the way).
And if all the above seems silly, describe your hardware which you use to connect:
cable/modem supplied by your ISP?
cellular?
router?
ethernet or wireless?
Are you moving around in the house and out of range of wireless?