One suggestion..... if you are using a USB keyboard then try plugging it into another port.  Some of the later BIOS updates for your model made changes related to USB.  Try using one of the ports on the rear of the system.  With most Dell models there is one USB port that is active during bootup prior to Windows loading and that active port is on the rear of the tower.

Thank you for this suggestion, Majestic.  I appreciate your time - and your effort.

Unfortunately it doesn't solve the problem though - my keyboard connection is the standard one (ie not via USB). 

And in any case the F12 boot function works fine (as does F8)... it is just the F2 (Setup Access) option that will not respond.

A few more suggestions then......  try tapping the F2 key as soon as the system has been powered up.  If that doesn't work then try hold a different key down when the system is powered up.  This may force a key board error which in turn may allow you to access the BIOS Setup to correct.   If that doesn't work then try clearing the NVRAM (CMOS).  In looking back at the BIOS history for your model there was a change related to "Updated keyboard key handler for setup" in version A05.  If you updated your BIOS from version A04 or an earlier version, this change may have a conflict with your present hardware setup.  Clearing the NVRAM (CMOS) should resolve that.  To clear the NVRAM (CMOS) on your model, click here for directions from your model's on-line service manual.  If that doesn't work then try another keyboard.  It maybe just a coincidence that the F2 key has failed after the BIOS update.

Ahhhh Majestic!!!  How we do trap ourselves (or at least I do)!

After receiving your follow-up suggestions I followed all of them to the full (including refreshing the CMOS) - all without success though.

Finally I did the thing I should have tried first: I used another keyboard.  AND IT WORKED!

So then I started to look for reasons why my existing KB wouldn't function.  It is relatively new - a very useful MS Multi Media device.  And that's when I started to kick myself.

All the function keys on this KB are dual purpose; in addition to their normal usage they double as short-cut keys to other functions.  For instance, F1 brings up Help, F2 is the Undo key, F3 is Redo - and so on.  A light globe was dimly alight!

There is also a key labelled F Lock (which I've never used before, and which apparently operates like the Num Lock and Caps Lock keys).

I'm sure you're way ahead of me now.

Of course I found that if I hit the F Lock key at the same time as F2 during the boot process, F2 works as F2 - not as something unindentified.

So all is now revealed!  I'll know better next time: i.e. look at the obvious solution first!

Thank you again for your research on my behalf.  I'm VERY grateful.