Zyxel wireless adapter is being used as an access point and the other computer sees it but will not connect to the internet? any suggestions?

Turn your DSL/cable modem off.
Turn your ZYXEL router off.
Turn your DSL/cable modem on.
Turn your ZYXEL router on.
Restart your computer.
You should now have an Internet connection.

Initial Set-Up
Plug your wireless router into the cable connection in your wall. Plug the connection cord into the "WAN" port on the router. Plug the router's power source into the wall and turn the router on. Connect your wireless access point to your router by pushing one end of an Ethernet cord into the WAP. Push the other end of the Ethernet cord into the "LAN" port on the router. The WAP connects your wireless devices to your router.
Connect your laptop or computer to the WAP. Click the "Start" button on your computer and then click "Control Panel." Click "Network and Internet" and then select "Network and Sharing Center." The "Network and Sharing Center" window opens.
Click "Set up a wireless router or access point." Click the "Next" button.
Follow the prompts to create a wireless pass phrase or security key. Write the key down in a safe location to ensure access later, if required.

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I'm NOT a Windows guru, but I think this is an issue with Windows, not your Zyxel driver.
There is a setting somewhere in the network area of Windows that tells it to automatically connect to a known favorite network if that network appears. I suspect you just have to find that setting, turn it on, and make sure the network you use is in your list of favorites.

try puuting the wireless access point on the middle and atleast 5 ft of the ground this will increase your signal slightly also make sure that there is no cordless phone especially the base near the wireless access point.

If you are able to "see" the network wirelessly, I would check to see if you are getting an IP address from the network. If not, chances are you are having an authentication problem. Having signal means the wireless adapter knows there is a network there, but actually connecting to it may require a little more. If you are using the Windows Connection, check to make sure there is a profile to connect to your network. Same if you are using a third party (in this case Zyxel) connection agent to see if there is a profile to connect to your network. You may need to speak to your IT people to see if they are using WEP or another encryption protocol; if they are, you will need the key to be able to connect and authenticate.

does the connection work on your router?(if you connect your computer directly to your router)

First many current PC models have switches to power on the wireless feature. Do you have one of those and did you power on the wireless.

Second wireless devices communicate on four different bands A, B, G, N. Some devices support multiple bands. Does your wireless router/access point (maybe a Zytel p660HW-D1 from above) support at least one of same bands as your laptop built-in or purchased wireless adapter? If you do not know post the manufacturer of the wireless router/access point, laptop if the wireless is built-in or wireless adapter if it is a separate device and I will check that for you.

Here is an article that should help -- there may be a issue. based on this article the Vista Computer is connected to the internet or ISP's network with a wire.

Ad-hoc networking access point

if you go to start then run and then type in that box cmd. Another page should open that has a black backround with white text. This is what DOS looks like. If you type in there ipconfig and no 192.168.0. If you don't see any 192.whatvever come up then I'm sorry to say it's your router. This happened to me recently.If not there it could be something simple like the ethernet cable, but I do think it's the router