<p>I'm trying to install the .Net framework version 2.0 on embedded Windows XP SP2 (aka XPE).</p>

<p>I'm using the XPE specific version of the installer from Microsoft:</p>

<p><a href="http://www.microsoft.com/downloads/details.aspx?familyid=c4837dad-5719-4b63-8752-cb0a65802329&amp;displaylang=en" rel="nofollow noreferrer">http://www.microsoft.com/downloads/details.aspx?familyid=c4837dad-5719-4b63-8752-cb0a65802329&amp;displaylang=en</a></p>

<p>When the installation starts it fails with the following error:</p>

<p>QFE Installer -- Error
Cannot connect to the database - please check the database</p>

<p>How can I get .Net 2.0 installed on SPE?</p>

Okay, so you're running the installer that is updating your XPE development environment, right?  Or are you attempting to run that on a device before you seal it?
You need to run that installer on the workstation that has the XPE dev environment (and database) installed.  The installer is looking for a specific database on a specific instance of Sql Server, so if you have (or somebody else has) changed it, you'll need to read up on how to specify the connection string to use with the installer.
In addition, it's probably trying to connect using your windows account credentials.  Make sure you are able to log on to Sql Server, open the DB with the component definitions, and add records to it.  Alternatively, if you can specify the connection string you can set a Sql login username and password to use.
Profiler is a great tool for troubleshooting the two issues described above.
Once you have the components installed, you'll have to add them to your image, check your dependencies and then build it.
If you're trying to just install .NET 2.0 on a machine directly (before you reseal it), you will need the packages for Windows Installer on the machine first.  There might be some other dependencies; I haven't done it in a long time so I can't remember.
The best way to troubleshoot dependencies on an XPE installation is to put ProcessMonitor from Sysinternals on it.  As you run the installer, you'll see where it attempts to find stuff and fails.  Take that information back to your XPE IDE and search your components for those files.  You then have to add the packages containing those files to your image and try again.  Its an arduous process sometimes..,.