Connecting a Mac directly to a cable modem is a very different configuration than connecting a Mac to a router that's then connected to a cable modem.
You should always describe exactly what configuration you have, and not worry about whether it's "simpler" or not at first. The problem is that an answer for one configuration may be completely inapplicable for a different configuration.
When you connect your Mac to your router, using the single ethernet cable you have now, which port on the router are you connecting it to?
Here are the tech specs for your router:
http://www.netgear.com/home/products/networking/wifi-routers/wndr3700.aspx#tab-techspecs
According to that page, your router has 1 WAN port and 4 LAN ports. If you plug your Mac into the WAN port, it won't work. You have to plug into one of the LAN ports. So that's the first thing to check.
Judging by this picture which comes directly from Netgear's website:
Image
I'd say the WAN port is the yellow one on the right, and the LAN ports are the group of 4.
Just to clarify what to expect, when you connect the Mac directly to the router's ethernet using your single cable, the resulting absence of a router-to-modem connection will disable all internet access. Anything that requires actual internet access will fail.
By breaking the connection between router and modem, you've essentially created a small isolated LAN (a Local-Area Network), which provides some wifi connections and 4 ethernet connections for local devices, but which is completely disconnected from the internet at large. This should be ok if all you're doing is trying to connect to the router's builtin web-page for doing configuration. But if something requires any internet connection at all, such as searching, etc. then that will fail.
