>Is there any way to re-register the event logs handler?
Only by uninstall and a fresh install.
I suspect there's something wrong with your Event Log. Try the following:
1.- Create a .VBS script with the following content:
Set WshShell = CreateObject("WScript.Shell")
WshShell.LogEvent 4, "Script started."
WshShell.LogEvent 0, "Script completed."
2.- Execute the script and then check if WSH events were written to the Application Event log.
Btw, if you restart the SL4NT service, are there event entries with Source 'SL4NT' logged or not?