There are plenty of IRC clients that should work fine on WinME. It should be significantly less demanding than the flash chat. Install Firefox 3 and try either ChatZilla or go to Mibbit.com Webchat perhaps.
Just wanted to let you know chevre, Mozilla dropped Windows 9x support with the release of 3.0
And to centende.
I suggest using mIRC, X-Chat, or a similar IRC program.
They are very light weight on resources (even compared to flash chat) and you can connect to more than just ADISC chat (though if you just want to stay on ADSIC's chat that's fine as well)