Sorry for the delay, but my mind has been somewhere else for a few days.
This sort of works, but not perfectly. It seems that the code is intertwined with the splash. When the latter is removed, the block changes and the login button goes to the far left. In my case, the block reverts back to my original image, which indicates I've put a bug in the CSS somewhere during my many experiments.
I actually overcame the login problem by creating a new page containing the login form and creating a block on the home page saying "Login - Members Only" with a link to that page. it works fine and the member doesn't have to make any extra hops to login.
Thus, from my perspective, I'm happy with the result and won't be trying to place the button on the home page any more.
This leads me to my last problem with the project. As it's a subject in its own right, I'll start a new thread.
Many thanks