SQL Server 2008 linked server to an Access 2007 DB that is in a protected directory on the Network
I'll just summarize all my comments here as an answer.

You should read this:

http://msdn.microsoft.com/en-us/library/ms143504%28v=sql.105%29.aspx#Use_startup_accounts

The SQL Server Service is the SQL Server engine and runs under an account specified for the service and linked servers which use a file share will necessarily use those permissions, since there is no setting to have the Server Service impersonate another account when it connects through the filesystem.

The SQL Server Agent is a separate process which runs scheduled jobs.  If you use this and it connects to network shares on its own (not just telling SQL Server engine to run some statement against a linked server which would be under the engine permissions above), it would need to run under an appropriate domain account.  In your case, that doesn't appear to be running, so I wouldn't bother fooling with it.

Running the SQL Server Express has certain database size and functionality limitations, and I wouldn't consider it for general server-class production use except for high numbers of lightweight servers - for instance a deployment of an small inhouse application to several worksites - where you wouldn't want to pay for licensing and the requirements fit the product.

The built in network account is "NT AUTHORITY\NETWORK SERVICE" and you can just put that in and blank out the passwords to restore it.

If you switch the SQL Server Service to run as a domain account, you will need to give it sufficient permissions to access the OS on the database server - i.e. folder access to where the database files are if the account doesn't have access.