Also check what dial up connection is set for collecting email from OE. If it is not the one that you specify, it may hang up and try to dial another. Somewhere in options, there is a command to pick up mail using a specified connection - it that one is not available, it will hang up the one that is connected. Sorry I cannot be more specific; I don't use OE but remember this from when I did some years ago.
When U open the Connection window in tools, on the General Tab U have a drop down tab with 3 choices. Make sure its on "Connect only when not working offline". If that doesn't work, I don't know. Sorry.