jtr,
Follow the Guide in this thread, lets see if we cannot speed up the WinME Machine for you:
Guide for Eliminating Spyware, Adware, and Random Popups
As for the ADSL, you do not actually dialup, you use PPPoE. I would recommend getting a Router which accepts a USB Connection from the ADSL Modem. Then go from the Router to each Comp via Ethernet.
Since the WinME comp is so slow, I would not connect yours to it until we have it fully checked for Malware.
Take Care,
Richard