Login failed for user ‘NT AUTHORITY\NETWORK SERVICE’. [CLIENT: <named pipe>]
Type: Failure Audit
Source: MSSQL$MICROSOFT##SSEE
Category: (4)
Event: 18456
User: NETWORK SERVICE

Rozwiązanie:

For supgraffix?s issue, based on the post, the errors are thrown repeatedly and there is an authorization problem in the configuration database.

I diagnosed that the issue happens in the Central Administration application pool account and the SharePoint Timer Service is not working properly.

There are both WSS 2.0 and WSS 3.0 error logs in your post. I suppose WSS 2.0 is the cause of your issue based on the database name.

To resolve the problem, you can do the following steps:
1. Browse to the SharePoint Central Administration page.
2. Under Server Configuration, click Configure Virtual Server for Central Administration.
3. Select Use an Existing Application Pool.
4. Select the application pool that the central administration virtual server is running under.
5. Click OK.
6. Run an IISReset.
7. Restart the SharePoint Timer Service.

W tym przypadku (pkt. 4) wybrany został:

StsAdminAppPool (NT AUTHORITY\NETWORK SERVICE).

Po takiej operacji restart usług (iisreset) nie wyrzucił żadnych błędów.