Hi Mike,
Thanks for the prompt reply. I have deleted everything and started again, by downloading SQLEXPRWT_x86_ENU again. I have run the exe and am installing again. Near the end of the installation of SQL2008R2 I get a message "Unable to find some components. Reinstall application" I click on the only option which is OK and the install appears to continue. After a short time I get the SQL Server 2008 R2 Setup Complete window to say that the installation completed successfully. This happened yesterday. How can I know that SQL Server 2008 R2 is in fact installed OK? Any quick checks I can run?

Remove the log file shown in this window. Highlight the log file in the lower window and click remove. Then you should be able to continue with the attach. SQL should then  recreate a blank log file.  What happens when you try this may help us understand the install problem.

Did the following
Unzipped NBNData_Data.mdf from install folder
Placed NBNData_Data.mdf in C:\
Opened Management Studio
Right clicked Databases
>Attach
In Attach Databases window
>Add
Navigated to C:\NBNData_Data.mdf
>OK
In Attach Databases window lower pane there are 2 files nbndata_data.mdf and nbndata_data_lg.ldf
Message alongside log file "not found"
Log file highlighted
>Remove
Clicked on OK to continue with the Attach.
Message "If you are certain that you have added all the necessary full-text catalogs, click OK. To add more catalogs click Cancel
>OK
Message "An error occurred when attaching the database(s). Click the hyperlink in the message column for details
>OK
Message - see screenshot

Didn't get beyond this so did not try a new R6 install

Nothing seems to work on this. I've downloaded and installed SQLEXPRWT_x86_ENU repeatedly. Everytime I delete then reinstall SQLExress 2008 R2 I get near the end of the install and I get error message "Cannot find some components. Please reinstall". I click on the only option which is OK. I get the same message again. Clicking on OK again permits the install to continue and I get the 'successfully installed’ window. Downloading and installing R6 again gets to the end of the process where I am "Attaching the NBN Data File" and I then get the error message which includes the line "File activation failure. The physical file name “C:\Program Files\Microsoft SQL Server\MSSQL.1\MSSQL\DATA\nbndata_data_log.ldf” may be incorrect”. I have tried extracting the NBNData_data.mdf file and attaching to SQL in Management Studio (Run as Admin) as per previous instructions. Each time I do this the log file is created with the Not Found message alongside. Removing the log file and then reattaching has the same result.

Presumably something to do with this version of W7 (?)

One problem is going to be that  from the screenshot it seems you have put nbndata_data.mdf in the root of  the C drive. This is a protected folder under Windows 7, so I  think this will cause a problem in reading the file and also in writing the log files. If you move this to another folder, it might allow it to be attached and once this has been done R6 may install.