Crikey! There is a lot more to getting the Silverlight Blue Prints for Sharepoint working than I expected.
You need to copy a lot of configuration into the web.config for your SharePoint web application.
Thankfully Patrick detailed what was required and provided a screencast of what needs to be done.
What to copy between the silverlight project web.config and the SharePoint web application web.config;
I put System.web.silverlight.dll into the GAC.
The other item is to register the .xap mime type. This seems to already be registered in IIS 7 on Windows 2008.
I could then add the web part.
I went to update the MIME type (IIS7)
Hmm, still not displaying the Hello World in the web part, and IE is crashing....
Problem Event Name: APPCRASH
Application Name: iexplore.exe
Application Version: 7.0.6001.18000
Application Timestamp: 47918f11
Fault Module Name: npctrl.dll
Fault Module Version: 1.0.30226.2
Fault Module Timestamp: 47c5c57b
Exception Code: c0000005
Exception Offset: 00025670
OS Version: 6.0.6001.2.1.0.272.7
Locale ID: 3081
Additional Information 1: fd00
Additional Information 2: ea6f5fe8924aaa756324d57f87834160
Additional Information 3: fd00
Additional Information 4: ea6f5fe8924aaa756324d57f87834160
At this point I decided to rollback my VM to the previous snapshot and try configuring it again.
I reconfigured the whole thing, but have exactly the same problem. The Silverlight app doesn't display and IE crashes as soon as I try to use it.
I will keep looking and post again when I find an answer.