what versions of Windows are on the other computers? if they are running Windows XP, you have to install a special updated LAN driver on your Windows ME machine. have you run the diagnostic software for the wireless card to make sure that it is able to establish a connection to your access point? have you checked the access point settings for encryption, etc?
I have a small wired and wireless LAN at my home connecting to the internet via DSL [ SBC ]. It works well using a router, etc.
I have several computers in the house that connect properly. My desktop, a P3 500, with a USB Linksys wireless access point also works well. However the access point and Internet Explorer on Windows ME do not communicate.