Poked a hole in the wall of my refrigerator. Is it toast?

So you just poked a hole in the plastic liner with the end of a wire shelf?
Um, fill or cover the hole.....AFTER you remove the offending piece.

if this is just a small pencil sized hole, it is not the cause of your fridge not cooling well. However the fact that not only is it probably a 37 year old fridge, but that you warmed it up to room temp yesterday in the dead of summer, wherever you're at, could both be contributors.
But not the hole.