Yeah NAT3 is definitely a problem for playing games. It means your router's firewall is blocking traffic.
If it's a NetGear router, I think it's likely that the login will be "admin" and the password will be "password". If someone has changed it, as Pope said, there will be a little reset button that you can press (with a sharp object like a pen) that will restore factory settings. Doing that means you will need to set up the internet connection again too.
Once you are into the router configuration, what you are trying to do get the router to do is...
1)
Assign a static IP to your PS3...every device that connects to your router will be given an IP at the time it connects. The number given will depend on how many devices are already connected.
So say for example you turn your PS3 on first thing in the morning, the router will most possibly assign 255.192.0.1. Now say you turn your laptop on in the morning then your PS3 after lunch. Now the PS3 may be assigned 255.192.0.2.
But you can tell your router to recognise your PS3 (via it's MAC address, which you can get from the XMB->System Settings->System Information) and assign it the same IP address each time.
2)
Put the static IP inside the DMZ...which stands for de-militarized zone, i.e. outside the firewall. It may be called a DMZ, or it may be a "firewall rule" or "firewall exclusion" or something else depending on your router. This will probably come with a warning that it's not a good idea, but you can ignore that because it only applies to PCs. Your PS3 will be safe.
3) Also, while you're there, if you use torrents, create a firewall rule for the port your torrents use and watch the speed go through the roof
Sorry for the long winded reply as it sounds like you probably have a good idea about most of this from your video tutorial. I'm really posting it more for anyone else who is NAT type 3 (or "blocked" I believe it is on the XBox).