Kevin,

See in-line

>I'm on WinXp Home. Is there even an Administrator acount?. I set up
>the users on this PC, with me as admin.

I've no idea.

>I used Windows authentication when I installed SQL Server. This should
>allow SQL to login using the Windows logon info, correct?

Yes it should.


>In the SQL Server Service Manager, there are 2 servers; one named
>after the PC name (MAROIS1) and another with the instance name I gave
>it MAROIS\SQLSERVER1.
>
>MAROIS1 is running, but when I try to start the other, I get the mesage
>'The service did not start due to a logon error'

Did you install two instanes?

>
>Should I have used Sql Server authentication? If so, what do I need to
>do set it that way?

It's good idea to have dev. SQL Server set up for Mixed mode authentication so you can troubleshoot login problems.

I would uninstall SQL Server and start over. This time install default instance only and apply SP3. After you get comfortable with SQL Server, you can play with instances.