Firstly, ignore Hyacinth's recommendation. The D-Link DSL-2540B is a DSL modem. This is cable Internet service. You won't be using a DSL modem/router with cable. Not trying to insult Hyacinth. I'm not trying to be mean. It's just not the right recommendation to make.
Secondly, you should not need to invest in any new devices. All you should need to do is forward the ports on the Netgear router for the games that you play. If that doesn't solve the problem, see if Time Warner will let you update the firmware on the router. Or have them replace the device.
The only other thing I could recommend is having Time Warner replace the device with a single port non-routing device such as a Motorola Surfboard modem, and then getting a D-Link DGL-4300, or a 4100. Plug the D-Link into the cable modem. Then enable Gamefuel on the D-Link router, and forward any ports you need to on the D-link router.
I've had Time Warner for quite some time, they should be able to offer you a single port device without routing.
One last thing....before you go ahead and do any of this, make completely sure that it's network lag that's causing your problems, and not game lag from having your settings to high, or not enough CPU, etc, etc.