Ok, so below you can find the output of sudo apt-get dist-upgrade, sudo apt-get update, and sudo apt-get -f update.
Hope you can help. I also have the stop sign on the upper notification area. It says that an error occurred. Actually system froze during an update a week ago or so. Current error says: 'Error: Opening the cache. (E: read error - read (5: Input/output error), E: The packages lists or status files could not be read or parsed.'
Error continued, but right now it has disappeared, so I cannot explain completely what it said.
Any help? Thanks in advanced.