Windows Service Pack 1 install problem

I am running (quite happily) Windows Home Premium but have tried on several occasion to install Service Pack for 64 KB976932 without success. I have done several fresh downloads of the Service Pack published on 4 April and tried to install and it gets to 99% and then fails and spends ages unpicking the installation. The error message I got was for the last attempt today was E_FAIL(0x8000405). I am using a Dell Inspiron Laptop. I have checked that the SP is not already installed and I have plenty of disk space.

Can anyone please assist me? As it is a SP I would be happier if it was installed and as it keeps trying to self-install and then deinstalling itself, I really would like it fixed.

Is it 8000405 or 80004005? As I am wondering if it might be THIS, in which case there is a hotfix listed there?

Thank you TrainableMan. This might be the fix if I understood it! I was quite careful in copying down the error code though and and it was - I am virtually certain - 8000405 not 4005. But even assuming I am wrong, why should I need a fix relating to a Server when I am just using one laptop with no other computers attached? I have had my new laptop about 18 months.

It's the only thing I found in searching, if that's not it then I'm afraid I don't know.
SQL Server is just a database and It gets installed for many different programs; I know it was installed on my machine for SyncToy to work.