Installed the SBS 2011 Premium Add-On (which is another copy of Windows 2008 R2 Server with SQL 2008 R2 on it) and moved all Sharepoint Foundation 2010 databases from the SBS 2011 server to the new SQL server.

In the SBS 2011 Application Event Log I kept getting an error message saying as below. The logs seem to happen at 2 minutes and 30 minutes past the hour so I'm assuming it's a Sharepoint Timer function generating the error.

The fix (I think) was to add the DOMAIN\SBS-SERVER-01$ account to the security public / sysadmin security role in "SQL Management Studio" on the server I moved the databases to.

You open the SQL instance in "SQL Management Studio" Navigate down to Security => Logins and add DOMAIN\SBS-SERVER-01$ as a login to SQL Server. I don't think you can browse to this account and do a "Check Names" on it but you just have to type it in.

My logs are now silent of this error:

Log Name:      Application
Source:        Microsoft-SharePoint Products-SharePoint Foundation
Date:          9/04/2013 8:02:09 AM
Event ID:      3351
Task Category: Database
Level:         Critical
Keywords:      
User:          SYSTEM
Computer:      SBS-SERVER-01.domain.local
Description:
SQL database login for 'SharePoint_ConfigurationDatabase' on instance 'SBS-SERVER-01\SHAREPOINT' failed. Additional error information from SQL Server is included below.

Login failed for user 'DOMAIN\SBS-SERVER-01$'.
Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
  <System>
    <Provider Name="Microsoft-SharePoint Products-SharePoint Foundation" Guid="{6FB7E0CD-52E7-47DD-997A-241563931FC2}" />
    <EventID>3351</EventID>
    <Version>14</Version>
    <Level>1</Level>
    <Task>3</Task>
    <Opcode>0</Opcode>
    <Keywords>0x4000000000000000</Keywords>
    <TimeCreated SystemTime="2013-04-08T22:02:09.755328400Z" />
    <EventRecordID>46901</EventRecordID>
    <Correlation />
    <Execution ProcessID="15148" ThreadID="12400" />
    <Channel>Application</Channel>
    <Computer>SBS-SERVER-01.domain.local</Computer>
    <Security UserID="S-1-5-18" />
  </System>
  <EventData>
    <Data Name="string0">SharePoint_ConfigurationDatabase</Data>
    <Data Name="string1">SBS-SERVER-01\SHAREPOINT</Data>
    <Data Name="string2">Login failed for user 'DOMAIN\SBS-SERVER-01$'.</Data>
  </EventData>
</Event>