You can manually re-run the update process and set it to record the results to text files.
If you post the text files back here it might show us what is happening.
To do this, open a terminal by pressing 'Ctrl' 'Alt' and 'T' keys together.
In the terminal window, type or paste in
sudo apt-get update | tee ~/"$(date +"%Y_%m_%d_%T")-apt-get-update.txt"followed by return/enter. Enter your password if asked.
Then type or paste in
sudo apt-get upgrade | tee ~/"$(date +"%Y_%m_%d_%T")-apt-get-upgrade.txt"followed by return/enter. Answer 'y' to any confirmation questions.
Running those commands should create two files called apt-get-update.txt and apt-get-upgrade.txt in your home directory.
The filenames will be prefixed with date and time information.
You can open them to check what they contain.
Post back and attach the two files.
