I've honestly never heard this one. I use trillian on my main pc on the standard msn port, and i can connect to msn on my pc with emule on. Infact there's 5 or so msn accounts running on my network and there's no interferance with msn.
I've never heard this problem. You might want to try the official
http://www.emule-project.net forums, if there's a known problem it will be there.
At a guess it could be:
1) a Firewall problem, ie. you haven't got the ports open correctly or are limiting to a certain number of connections
2) Poor software/firewall that isn't allowing connections
3) Weird bandwdith usage. Cap your upload on emule about 10-15% below your line maximum. Doubt this will do anything but you might just be using too much bandwidth (it should be more noticable that you can browse the internet either if this is happening).
4) If you use a router, you might be opening too many concurrent connections
As i said, those are just guesses though.