Oh noooo!! I've been trying to sort out a similar problem on a friends PC for ages now.
First, have you checked that Outlook Express is not set to disconnect after sending / receiving? It's set by default to do so, so you have to turn it off (in OE) in Tools > Options > Connections.
Next go to IE Tools > Internet Options > Connections > Settings > Advanced, and make sure nothing is set to Auto Disconnect.
Try those first, Lona, and come back to us if it doesn't help, then we'll have a look at your Modem Speed and Port Settings. If you know how to change these, set them both to 115200. That might help.