I changed the monitor from an old Philips TV set to a newer Samsung - both with HDMI ports.
Using the Samsung, I can now get into the BIOS using F2.
I have no idea why this makes any difference - I use the Philips monitor with other PCs.
Using a MEMTEST boot stick it works just fine - I can see all the MEMTEST menus.
So, now I suspect that the Win 7 boot memory stick is faulty.
I see mention of UEFI and Legacy!! - needs some research.
If I still have a problem, I'll open another thread.
Closing this now.