Ok, this is going to be a slow process as we seem to be on different schedules East coast vs West coast.
The default gateway is 192.168.0.1 This is the IP of your router. My understanding from the Netgear site and personal experience is that wireless Netgear routers have an IP of 192.168.1.1 but we will proceed.
Type
http://192.168.0.1 into your browser. You should be presented with a login screen. Your user name is "admin" and your password (unless you changed it) is "password". If you are not presented with a login box, try
http://192.168.1.1 I know you've already been in the config screens before so please bear with me if I'm telling you things you already know.
Once in your router's config screens, select "Basic Settings" from the left column. It may already be on that screen. I'm guessing you have a check for Yes in "Does Your Connection Require A Login? There will be a user name and password in the fields provided. Please confirm this yes or no.
If I am correct, your router is set up to log you in automatically.
Take note on the left hand side of "Port Forwarding /Port Triggering". This could be very helpful to you in the gaming you want to do. From the website I linked for you earlier, there appear to be numerous ports that need to be opened. Port Triggering could be helpful also. There is an explanation for every field on the right hand side.
Also look at Dynamic DNS. I have seen some of your other posts and this could be extremely helpful for you with the Dynamic IP you have. You can set this up so your WAN IP is reported to the dyndns.com site and your friend can access your computer by simply typing a URL into his browser. The basic service is FREE too!
Right now I just want to confirm that your Router is doing your login for you.
Edit: From what I can gather it appears your modem can also function as a router. The IP for the config for the modem is 192.168.1.1, which is why your Netgear has been changed to 192.168.0.1. You will need to have the modem only connected to the computer to access the config.
I would suggest letting the modem perform only the pure modem functions and let the Netgear take care of DHCP, DNS, opening of Ports and the login. Here's a
link to help with the modem config. To test out internet access with the modem only, you will have to config it as such.
You will know when you have it right when your Default Gateway and DHCP server is listed as 192.168.1.1. I'm thinking your Netgear is configured to log you in and your modem is not. This is why you can't connect just using the modem.
I'm going out of town soon, so my help will dry up.