Getting timeouts and backup errors after mirroring and log shipping is setup
If your server has only  4GB of RAM, AWE isn't going to help you much.  AWE is designed for when you have greater than 4GB of RAM you need to use.

Timeouts are harder to define.  The timeout period itself is likely defined in your application, so it's not inherently SQL Server that's causing the timeouts.  However, what you're running into are queries that take to long to complete.  To troubleshoot this, I would first start by reviewing the wait stats to identify specifically what is causing things to drag in your SQL Server.  Some waits to look for:


BACKUPTHREAD means your queries are waiting on backup operations to complete.  Other backup waits could indicate problems.
Memory pressure could be any number of waits, but look for things like RESOURCE_SEMAPHORE or IO waits.  Also, check the trend on your Page Life Expectancy in Perfmon (SQL Server: Buffer Manager -> Page Life Expectancy).  If this continually trends low, your pages are cycling out of memory to quickly.


Another thing you can do is check how long your log shipping backups are taking to complete:

SELECT 
    database_name
    ,backup_finish_date
    ,datediff(ss,backup_start_date,backup_finish_date) SecondsToBackup
FROM
    msdb.dbo.backupset
WHERE
    type='l'
ORDER BY 
    backup_finish_date desc;


As for resolution, if your log shipping is happening all at the same time, you might want to try and stagger that out.  If it isn't necessary to log ship every 5 minutes, I'd try and go with your 15 minutes and stagger each database off by 5 minutes so that they're running separately.

The other thing is to consider a hardware upgrade.  The box your describing sounds fairly out of date, considering there are laptops you can purchase now that have more horse power than what you're describing.  If you can move the server to a virtual machine, you'll be able to immediately upgrade to better resources, which could resolve these issues for you.