I may just be luckier than technically adept, and I wouldn't say it's completely fixed - you may be trading one problem for another. Here is what I did:

1. Copied all of the SQLDataProvider files with a version greater than or equal to 03.02.06 in \Providers\DataProviders\SqlDataProvider to a different directory
2. Used a text editor to find and replace the database owner and object qualifier data - use an editor that can do it in every file at once for less pain.
3. Run the 03.02.06 file in Query Analyser
4. At this point it was no better, so I looked around and found a post about the app name hard-coded in web.config causing problems. I changed it to "/" (look around line 200) and was able to create some child portals.
5. I can back later and couldn't log in. This was the problem in the log, although I didn't know to this detail until I fixed it:
   AssemblyVersion: 04.03.01
   Method: DotNetNuke.Security.Membership.AspNetMembershipProvider.UserLogin
   FileName:
   FileLineNumber: 0
   FileColumnNumber: 0
   PortalID: 2
   PortalName: XXXXXXXXXXXx
   UserID: -1
   UserName:
   ActiveTabID: 88
   ActiveTabName: Home
   AbsoluteURL: /Default.aspx
   AbsoluteURLReferrer: http://XXXXXXXXXXX/Home/tabid/88/ctl/Login/Default.aspx
   ExceptionGUID: cb47c030-343f-40df-971a-6c98fbac64e6
   DefaultDataProvider: DotNetNuke.Data.SqlDataProvider, DotNetNuke.SqlDataProvider
   InnerException: Object reference not set to an instance of an object.
   Message: DotNetNuke.Services.Exceptions.PageLoadException: Object reference not set to an instance of an object. ---> System.NullReferenceException: Object reference not set to an instance of an object. at DotNetNuke.Security.Membership.AspNetMembershipProvider.UserLogin(Int32 portalId, String username, String password, String verificationCode, UserLoginStatus& loginStatus) at DotNetNuke.Entities.Users.UserController.ValidateUser(Int32 portalId, String Username, String Password, String VerificationCode, String PortalName, String IP, UserLoginStatus& loginStatus) at DotNetNuke.Modules.Admin.Security.Signin.cmdLogin_Click(Object sender, EventArgs e) at System.Web.UI.WebControls.Button.OnClick(EventArgs e) at System.Web.UI.WebControls.Button.RaisePostBackEvent(String eventArgument) at System.Web.UI.WebControls.Button.System.Web.UI.IPostBackEventHandler.RaisePostBackEvent(String eventArgument) at System.Web.UI.Page.RaisePostBackEvent(IPostBackEventHandler sourceControl, String eventArgument) at System.Web.UI.Page.RaisePostBackEvent(NameValueCollection postData) at System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) --- End of inner exception stack trace ---
   StackTrace:
   Source:
   Server Name: XXXXXXXX
6. I thought perhaps I'd better run the rest of those scripts - maybe it would help. It didn't get me logged in, but I believe you should still run them anyway - do them in version order, of course.
7. Had I seen the exception above, I would have immediately changed the web.config back so that the appname was "DotNetNuke". I did this and was able to log in.
8. I was also able to create a new child portal!

It gave me a bit of a scare this morning when I didn't log in the first time, so I'm not sure it's all fixed.