When I press F1 in Adobe Reader X 10.1.3 (in Windows XP and Windows 7 Pro), it instantly takes me to http://helpx.adobe.com/reader.html in my default browser.
Where/how do you get that error message - as a popup, or in your browser?
F1 brings up the exact same message for me, "Online Help content cannot be displayed. Verify you can launch your web browser and have access to the Internet". The message appears within Adobe Reader X. It doesn't reach the browser at all.
When I click Help from the menu bar followed by Adobe Reader X Help, it will take around 5 seconds to have a think, and then show the message. I've used the setup assistant to set to default and no change. In Preferences, the Web browser Options for the Internet are all ticked,
I have never seen that before; can you try to repair Adobe Reader (from the Help menu)?