It looks like you are unable to log into your site, so going to Admin > Log Viewer is out of the question.

The error indicates that there is something missing in the portal settings or portal alias. I recommend examining the records in the Portals and PortalAlias tables for your site. If you can compare these records to the records in a working DNN database that would help.

If you change the data in either table you may have to "restart" DNN for your change to take effect. To do this, open the web.config file (which is in the root DNN folder) in Notepad, and resave the file (without making any changes to it).

Another idea:

The method that is causing the problem is:
DotNetNuke.Entities.Portals.PortalSettings.GetPortalSettings(Int32 TabId, PortalAliasInfo objPortalAliasInfo)

I think the error "Object reference not set to an instance of an object" indicates that when DNN calls this method nothing is returned. Now this method I believe calls the SQL stored procedure GetPortalByTab (this is my guess because the parameters match the method's parameters). So why don't you run this procedure and see if you get 0 rows back. I am guessing you will, so then the next step is to look at the SQL of the procedure and figure out why it is returning 0 rows.

You need to run the procedure with the TabID of the page that should be loading when you start DNN, and the address of your site. You can find the TabID by running SELECT * FROM Tabs. For example:

exec dbo.GetPortalByTab 36, 'www.mysite.co.uk'