Modem when used for fax does not connect to anything (no network connection or dialup internet connection). It just keeps listening to the line. If it gets a fax it receives the document over the telephone call. A fax is like a telephone call, only instead of someone's voice you get data.
So you can connect your PC to telephone line via modem and set up PC to receive/send fax; and use high speed internet at the same time.
To connect to your PC, would be like accessing your files over the internet. If you are using Windows XP and later, then you can use Remote Desktop to remotely log in to your computer. Here is how : http://www.microsoft.com/windowsxp/using/m...emoteintro.mspx