Open terminal ad run sudo apt-get update. Then run sudo apt-get upgrade. It
should then tell you whats wrong. For me it has suggested to run sudo
-fixmissing. Then run udate and upgrade again and it shoul fix it. It has
worked for me, hope this helps

I ran sudo apt-get update but I did not see any errors.
When I ran Synaptic again, though, everything downloaded and
installed without any problems.

sometimes just runnimng apt-get will fix things that you cant do anywhere esle..
Apt-get is probly the best way to update. Glad yours is now working.