I have successfully extracted the old machines and rearranged my desk to create much more space -- although I will have to do some serious filing and discarding to reduce the enormous pile of stuff that is sitting to my right. And everything is working well.
Except that I powered down the NAS to make sure I didn't cause it any damage by accidentally unplugging it. And when I touched the power button accidentally, it made a crackling sound and emitted a bad smell.
I think the power supply is fried. And a new power supply is over $100, which is maybe not money that I should put into this particular box.
Then there's the question of salvaging the disks. I think that everything that's on them exists somewhere else, because this was the backup drive.
But now I need to get something running and make a fresh backup.