Thanks for the replies!
I have also NEVER used a grounding strap when working with a PC by itself (not that using one is a bad idea; I certainly don't want to discourage people from playing it safe).
I have replaced hardware many times, including entire motherboards etc.
Instead, I always made sure to
a) discharge any static by touching the metal of the case before touching anything else
b) not to build up static (i.e, I made sure not to move my legs or body on the carpet, if any, while working on the PC).
This thread, however, was about a special situation, involving more than just the PC and its components.
Everything worked out.