I found this What??? You deleted "Default Web Site" from IIS?!?! had some useful info.
In particular (as per the article), to check that it really has gone:
"First you want to really make sure that there is not a web site known as W3SVC/1. Who knows, maybe someone had simply renamed your default web site or something. Open a command prompt and type this:
cscript adsutil.vbs enum w3svc/1
If it comes up with "The path requested could not be found" then sure enough, you don't have a true default website anymore. If no error then check out the "ServerComment" to know which web the machine now thinks is the default."
OK - so its really gone. You can follow the rest of the article or simply recreate another one.
I decided to re-install IIS - who knows what else was screwed up?
Control Panel / Programs / Turn Windows features on or off.
Uncheck all the IIS stuff. Then OK - it's all removed.
Then check it all back again - OK - IIS will come back and you may or may not have a "Default Web Site".
If you don't, just add one - there's nothing special about it - it's just another web site.
Start / Administrative Tools / IIS Manager
Right click Sites / Add Web Site
Call it "Default Web Site". Point to:
C:\inetpub\wwwrootYou should now have it back - along with others that may have been in that directory.
Click "Default Web Site" / "Advanced settings". Check that the ID is 1. You are good to go!
If you use ASP.NET and .NET Framework 4 - beware!
Look here: ASP.NET : Handler “PageHandlerFactory-Integrated” has a bad module “ManagedPipelineHandler” in its module list