I can't tell you what happened butnever ever use startx in "Recovery mode" - never ever - you are root and will continue to be root
Furthermore please use mintUpdate for updates/grades as the possibly dangerous updates are sorted out.
And if you cut power during such an operation things may go really wrong
In "recovery mode" run
to complete the upgrades that failed.
Update should not give an error message while you should receive an error message from upgrade
Please don't use these commands normally, instead use mintUpdate
Now you have already started the process.
I guess that an error message will tell you to run
dpkg --configure -a
You may also have to run
apt-get install -f
All in recovery mode - in normal mode you need to precede the commands with sudo
Leave recovery moder with a reboot or by typing exit