[ubuntu] 15.10 to 16.04 upgrade borked my installation

I don't know what happened; the upgrade was proceeding and all of a sudden I got a blank screen. When I rebooted and selected Ubuntu on grub, I got a bunch of text referring to the sda partition, which got repeated a few times. Never went any farther. I then prepared a live 16.04 (64 bit) usb and booted from that. No problems, but I couldn't repair the borked partition with the live usb. I tried the instructions provided here, but it couldn't mount in /mnt anything but the root partition. Is there some other way I can proceed, or am I now stuck reinstalling from scratch? Incidentally, the computer is an Intel iMac, and I was ruing with a second monitor.