I had the similar problem in Fedora few years ago. I upgraded packages then in steps by alphabet. And restart after every step. And then X server wont start.
Then I start Linux in text mode. (not sure, if this is right name for this.) And continue to upgrade packages in text/console mode. System is recovered.
Maybe is this solution also in Mint.
Indigo Pony? Alas, what you go through these days!