Any chance you'll be upgrading soon? 😄
At 10.1, you can make a Database Connection to the database, use the data from the database on your map, and publish a map service.
At 10, you can connect to your database by creating a query layer in ArcMap, using the data from the database on your map, and publishing a map service.
At 9.3.1, connections to databases that don't contain enterprise geodatabases are limited to OLEDB connections. If you have x and y values in the table, you could create an xy event layer to render the data in ArcMap then publish a map service...but you can't access spatial data directly and publish it.