Yes, just pushing the button in puts the Nook into sleep mode. Things can still run, and the wifi connection circuits will still draw power unless you manually turn off the connection in Settings. If you hold the power button in for about 5 or 6 seconds, it will pop up a box asking if you want to turn it completely off. If you tap 'Yes', it will fully turn off. But if you then plug it into the charger, it will turn back on again, since it apparently must be at least in sleep mode to charge.
There have been sporadic reports of browser freezing lately, although I haven't had that problem since the ver. 1.41 upgrade a couple months ago. If you haven't already, you might try downloading the Dolphin Browser HD from the app store. It's free, and a nice browser. That would give you something to compare with, to figure whether you have a software problem or a wifi or hardware problem.