I'm suggesting reinstalling using a USB. You will have much fewer headaches that way. Does your BIOS allow for booting from a USB drive? Just grab the Ubuntu image writer (startup disk creator) from the repositories and use it to put the ISO onto a USB. It will be exactly like a live CD without the CD part. Then just reinstall your system. If you have a separate /home partition, then don't reformat it, just use it as it is. If you don't have one, now would be an excellent time to make one.
You could just get the packages and upgrade them, but it will cause problems. I've never had good luck with in-place upgrades on any system, Linux or otherwise. That's why Mint doesn't allow for it with the stock upgrade manager.
Running on a 4-slot toaster @ 60Hz