If you can establish a remote desktop connection with the machine, then do that and, rather than just looking in the Event Viewer, open up IIS Manager and browse to your website.
For me, this will often show an ASP.NET yellow screen error identifying any required files that have not been included within your deployed Azure package. You should mark those files as "Copy Local=true" and redeploy - you may need to do this a number of times to catch all of the missing files.