You spurred me on to have another look into what drivers I was using. I went to the HP site and noticed that they have Windows 7 AMD drivers (AMD = ATI - AMD bought the company). I was using a 2008 version which I've now upgraded to the 2009 version - 8.593.100.0 (21/05/2009) (version on HP site at this time is: 8.593.100.5090521A084776C (20 Nov 2009)), and lo and behold the sprites are now visible in the layout designer view - WOHOOOO!! Thanks for saving me ���� as I wasn't quite ready to go out and buy a new laptop.
For anyone with similar issues this is a link to the HP site for the HP6910p video driver. Note that I have Windows 8 Pro 64-bit installed on this machine.
HP 6910p Video Driver site link
Here's a link to the main page for the 6910p HP support page which contains plenty of updates.
HP 6910p Support Page
BTW, after updating the driver and restarting Construct 2, I noticed that two of my sprites didn't display until I resized them in the animation editor. They were larger in size and were being scaled in the layout view. If they needed to be scaled down they were invisible, however, once I resized them in the animation editor they displayed perfectly in the layout view. The same problem exists for some of the demo project sprites, but at least I can work around it now.