If you have a lot of neighbours with networks around you then there is a good chance they are all set to default and may be limiting your connection, so what we need to do is change the mode and channel assignment on your router to see if we can get you a stronger signal so that your other machine will then pick up on it cleaner.
If you have already setup security and setup a unique name skip those parts of the instructions.
To do this can you go to a machine that can get online through the router using a hardwire then click Start and then Run and in the Run box can you type CMD then hit enter to open a DOS window.
From there can you type ipconfig then hit enter and make a note of the Gateway address which should be something like 192.168.1.1
Once you have that can you open a Internet Explorer Window and type the gateway address in the following format http://192.168.1.1 then hit enter to open the routers login page.
When prompted type your admin username and password ( If you have not changed it just leave the username blank and enter admin as the password)
When you get logged into the router can you click the Wireless tab then enter a unique Network Name then save your changes.
Once that is saved can you then click the Wireless Security link under the Wireless tab and then choose the type of security you wish to use such as WEP then choose 64bit and enter a 10 digit number in the Key1 box (if in doubt just use your 10 digit phone number with area code) then save your changes.
After it has savedcan you then go back to the wireless window and choose Wirless G only for the Wireless Mode then change the Standard Channel to 1 or 11 and save your settings.
Once all that is done can you then wait about 2 minutes and see if you can connect your wireless machine and then test it for 24hrs or soand let me know if you see an improvement or not.