There has been a lot of comment here to the effect that you need to
chain yourself to your work before daring to let thoughts of opening the
carton containing memory, cards, etc. OK, I exaggerate; and I do agree
that precautions should be taken against static, and machines totally
powered down before plugging things in. The danger is not just of
totally destroying things (not too serious, just replace), but of
causing more subtle damage which doesn't show up immediately.
But we've all seen fairly careless handling of bare electronics, and
working on the innards of plugged-in ATX machines, with little trouble.
I am reminded of the book, years ago, about the development of a new DEC
machine ("The birth of a new machine" or something similar). There was a
desperate rush on, and everyone regularly plugged in and removed
ordinary DIL chips with no precautions. While CMOS chips may be more
static-sensitive than TTL, I don't know whether they are more vulnerable
to plugging in like this. My own experience is only of removing and
inserting PC BIOS chips into running machines (after a failed BIOS
reprogramming); never any trouble.
And there is a PCI standard designed to allow specially designed cards
to be plugged in and removed from a running machine (24/7/365.25 server,
typically).
I don't want to take the risk, but I wouldn't be at all surprised to
find that (un)plugging ordinary PCI cards live, and other things, are
only slightly hazardous.
On the other hand, I have heard of PC motherboards that were blown by
plugging in a keyboard (DIM connector).
I'm not advocating that these things should be done, but don't feel that
you have necessarily caused irreversible damage if you make a mistake.
Best wishes,