Barry,
You need two things:
1. You need a road network on which to compute the network distancea and
2. You need locations from where to compute the distances.
Looks like you have 2. You can start with addresses, geocode them and turn them
into a feature class. You do not need to build them into a network dataset, etc.
So what you need is 1. a network dataset. A free one comes with ArcGIS. It is called
StreetMap and you may have to install it from your data and maps dvd/cd
Once you have that, add the streets to ArcMap, turn on the NA extension and add the NA toolbar. Add your locations (feature class) to ArcMap, Create a CF or OD layer from the NA toolbar and use that to comptue the one to many routes or distances as needed.
Jay Sandhu