I was installing the Access front-end and SQL Server 2005 Express back-end application on a client's network (Server 2008) and found that the Access program could not connect to SQL Server from a PC either through an OLEDB connection string or a DSN connection when logged in as a user. However the exact same OLEDB connection string and DSN worked perfectly when logged in as Administrator.

How would I be able to tell if this is a Windows Server issue or an SQL Server issue? Thanks!

Sounds like an SQL Server permissions issue.