Well, every time you reset it, you put it back to factory settings. So when you keep having problems, it's likely because you're fucking something up in the settings. (edit: re-read it and it looks like you can't even find the router's config page, so yeah... definitely gonna need that model number)
First of all, NETGEAR is the default SSID for these routers. When you reset it, like clean, out of the box, you get NETGEAR. Since "NETGEAR 2" keeps popping up, that must mean that it's an advanced feature of this router that enables you to have multiple SSIDs. That's a good thing. Learn to use it. But the fact that you keep seeing NETGEAR means you are reseting your router successfully. That is to say... you achieved your goal of resetting it.
Before I smack you upside the head, I should mention, there is a slight possibility that the router's hardware is to blame; Netgear doesn't exactly make the most stable and reliable hardware. It might just be going dead. I just replaced a dead Netgear MIMO-G router for a friend yesterday. It would lock up/restart every time anything tried to use the internet. So it might not be your fault, but that would be a locking-up problem, not a NETGEAR 2 problem.
So, with that said, I'd need to know the model of your router, so I can Google an interface emulator for your model router, or a user's manual, and I can read your manual, and tell you what you need to do to set up your router properly. It's on the bottom of the router, and it's just one of those things you really should know without looking (like that I have a Linksys WRT54GL here)...
Edited by FalconFour, 28 November 2010 - 08:10 PM.