Is your modem external or internal, nowadays they should all be internal.
Check you settings and see if "wake up on Modem" is enabled or disabled. It should be disabled. not many peopel have a use for this being on any way.
Windows ME does not have a very good driver database. If you cant get it to work, try searching for new drivers. I would even try drivers designed for windows 98 as it is a very similar operating system to ME.