Also turn off your antivirus software. Sometimes it gets in the way of the Internet.
Uhhhhh . . . I thought the same way you do. That's the only time I was wrong calling ISP tech support. I called to say that the new WiFi USB key (this was a few years ago) that I'd bought for my mother would get recognized, would connect and get DHCP but nothing more, so the problem was obviously on the router end. The first thing the tech asked was for me to turn off the antivirus. I fudged and said sure, ok... it's off... still doesn't work. The tech then quickly walked me through a series of lengthy MS-prefixed DOS-mode commands, and hey presto, no more problem. I asked what he'd done. He said he'd turned off my anti-virus. The driver for the big-name USB WiFi key wasn't signed, so Norton interfered with it. I told my Ma to buy another antivirus. The tech support was good (this was the guy who first picked up the phone), but sorry for most of you, it wasn't in the U.S. (it was French Orange). They'd got better since the day they told a friend of mine to restart Internet Explorer after he told them he'd diagnosed a failed route in their peering exchange.
And that is not the time when I installed a totally clean computer for my aunt who'd provided me with original CDs of Windows, Norton, et al., connected it to the Net, and the first popup was "Norton has detected that your system is trying to access the Internet, recommend Accept". I wondered what it could be, so I clicked for the details, and the packet in question was "incoming to port 135" from an IP somewhere in Africa.