The "Y2K" problem (actually, a raft of problems most of them to do with outdated human procedures) required a few lines of code be added from a Cobol perspective. It took longer to identify them than to fix them in most cases, and the enterprise in which I work experienced two consecutive waves of date rollover problems because we keep track of very old things (people).
Coding for the century rollover was almost trivial, the time involved mostly due to a database update time-suck.
I don't know of a single shop that used the advent of Y2K to throw out their obviously useless Cobol programs and kit out with new (whatever).
Neither do I know of any bank whose ATMs stopped working on New Years Day (the big Y2K Gorilla in the Room).
There were a few ATM booth door locks around here that wouldn't function, and a couple of our UPSs shut down pending a code update, but the machinery in them wasn't running Cobol.