I'm not sure about Win ME, but do you have a program, the same as in Win 98 called System Information? If you do it's located in System Tools.
If you have this program, open it and open Hardware Resources, then look down the list for IRQ's and open it. This will give you a list of all the hardware and what IRQ it's using and what it's sharing with. See if you can see either the modem or COM3 in that list, you should see who the culprit is that it's sharing with.