I have been taking images of coins for collectors for 3-4 years. I use 100 and 180mm macro lenses.
I have the camera powered up via an AC power adapter and use a remote to trigger the shutter. I enable the mirror lock through the menu C.Fn III-13: Mirror Lockup > Enabled. This has worked without a problem for the past month. Different shutter speeds work perfectly, both before and after the current problem.
When Mirror Lockup is enabled there normally is the click, a delay of a couple of seconds and then the shutter is activated. When I went back to work after a break, the shutter activated immediately, not with the usual delay. Since I am not using batteries (Canon ACK-E6AC Adapter Kit) there is no battery to take out and discharge. I will take the coupler out and then back in to see if this resets it.
I am not using either the built in flash or any external. With the exception of the mirror lock not working, everything else is working normally. I haven't applied the latest firmware yet, but only because it seems to be a fix for flash issues.
Thank you for your comments. They are much appreciated.