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I tried different computers with the Arduino IDE previously but could never get the original Meduino Mega, or a spare I bought at the same time, to enter programming mode. One of those mysteries and not worth losing sleep worrying about why.

Hi Dave,

Have you contacted the seller of the Meduino Boards?
If it happened with two boards of the same batch, maybe they had a problem. Seems the bootloader isn't installed.
You could also try burn a bootloader on them from Arduino IDE.

I'm glad to know that your system is now running OK.

Rgs.