It has been long enough since I opened the case for this computer that I had forgotten how the drives were mounted. In order to get the failed drive out, you have to remove the front panel. This isn't *hard*, but it *is* tedious, especially when there isn't a good place to work. But I managed to wrestle the drive out (once I figured out which drive had failed) and install the new drive.
The motherboard RAID software figured out that the new drive was there, so when I booted into the control software, I was able to tell it to start restoring the mirror. Then the system booted on into Windows where everything is now running *very* slowly as the disk subsystem is spending most of its time making a copy of all things on the old drive to the new drive.
Looking at the situation, I have now ordered a *second* new drive that will arrive Sunday, by which time, the mirror should have reestablished itself. Then I can remove the remaining original drive, put the second new drive in, and let it mirror everything again.
And then I will finish putting the computer back together...