ZyXEL NBG334W Wireless Problems

[liz16-2008]

I have a ZyXEL NBG334W wireless cable router, and have just worked out how to set it up to connect to the internet via the modem.
E.g. the LAN is connected from the laptop to the router, which is then connected to the modem.
This took a fair bit of time and involved complicated things like changing IP addresses.
Plus, when I remove the LAN from the laptop, the internet stops working, I'm not too sure if this is supposed to happen as I thought the wireless ZyXEL thing would mean the internet could operate on the laptop without being plugged into it. I could be wrong, as I said I'm not sure.
The problem is: I have another laptop and I would like to set up the internet on it, but without having to connect to anything as this laptop would be situated two floors above the one plugged into the modem.
Has anyone got any idea of how to do this? I have tried many different things without really knowing what I'm doing. If anyone could give me a step-by-step guide with simple-ish language as I'm pretty thick when it comes to computers, then that would be great.
Thanks for your help

[liz16-2008]

More Info:

For some reason, even though the ZyXEL router is wireless, it doesn't seem to be able to connect with anything wirelessly. When I try to connect it says there is no response, even though the green bars are full.
The signals on the ZyXEL itself say:
Power: Green Light
Port 2 (which is connected to the modem by the LAN): Orange Light
Internet: Flashing Orange
Wireless: Green

When I click "Connect To" via the Start menu on the laptop I want to set up wirelessly, it gives me two options (sometimes others appear but these are the main ones which are generally always visible:
fire211261wall - Security-enabled network - Green Bars full
(Extra info shown when I hover:
Name: fire211261wall
Signal Strength: Excellent
Security Type: WPA-PSK
Radio Type: 802.11g
SSID: fire211261wall)
SKY35416 - Security-enabled network - Only One Green Bar
(Security type & Radio Type same as other one)

The second option I don't choose as it doesn't seem to be anything to do with my internet, plus it has poor connection.
On the other hand, the SSID I gave the ZyXEL when I set it up is fire122161wall. So naturally, I click on this one.

It asks me for the passphrase, so I enter the one that was given to me when I set up the ZyXEL.

Then it says "Connecting to fire122161wall"

And then it says "Windows cannot connect to fire122161wall"

I diagnose the problem, and it says "Wireless association failed because Windows did not recieve any response from the wireless network"
Which is bizarre as it earlier stated the signal was strong
So is there something wrong with the ZyXEL itself?

Also, I tried setting up a network on the laptop which is manually connected to the internet through the ZyXEL. I called the network "DOWEN-OFFICE_Network" and wrote down the passphrase.
This seemed to be successful - until I put the flashdisc which had saved the network into the other laptop.

It asked me "Do you want to add the computer to the wireless network "DOWEN-OFFICE_Network"?" and I clicked OK.
Then it said "You have successfully added this computer to the wireless network "DOWEN-OFFICE_Network"."
The only problem was...it hadn't. There was still no internet connection!

Other information that might be useful (I really don't know how useful any of this may be, but am including everything I can think of)

On Laptop One, the one connected to the Internet manually through the ZyXEL, when I click on Manage Network Connections it gives me two:
Local Area Connection on Network 3
and Wireless Network Connection, which has full green bars but isn't connected.
When I try and connect it, it gives me three options: fire211261wall, Unnamed Network and _ZyXEL. Neither of these work.

On Laptop Two, the one I am trying to connect to the internet wirelessly, when I click on Manage Network Connections it gives me two:
Local Area Connection, Network Cable Unplugged
and Wireless Network Connection, which again has full green bars but isn't connected.
When I try and connect it, it gives me one option:
fire211261wall. This doesn't work either.

There's nothing else I know of to include. If you need more complex information you'll have to tell me how I can get it I'm afraid