I have the same tractor about the same vintage - and a few years ago I had the same problem. I diagnosed it to the glow plug relay - and got a new one, plugged it in, and it's been good since then!
An easy fix - and I hope yours is easy too!
Ha - just read your post about hooking up the battery wrong, and I did the same thing on my wife's New Holland TZ25da - as the battery lost power and needed to be changed.....well, it turns out that after changing the battery that the alternator was not charging, so after having problems finding...