Did you run Boinc as well as Boinc Manger?

Check that Activity is not set to Suspend, or that the project is not suspended and check your advanced preferences; Processor usage, computing allowed when computer is in use, use GPU when computer is in use and while processor usage is less than (might be 25, best at zero).

If these fail, do another full restart.

Well, you did manage to complete two tasks today. Perhaps you did a driver/system update?
Do you have a full hard disk installation of Linux – you’re not booting to USB?
You can start Boinc without starting the Boinc Manager, and while the Boinc client should start when you start the Boinc Manager I found that it sometimes did not, so I always started the client first, not that I have Ubuntu installed at the min.
Before shutting down, do you exit Boinc?

There is no need to suspend projects before exiting Boinc, just exit Boinc first and it should close running applications, but you could try Advanced, Shut down connected client, then close Boinc Manager and shutdown or restart the computer.
Within the folder you downloaded Boinc into there should be a file called boinc. Try to double click it before opening Boinc Manager, to see if your projects and tasks are there. If they are not try to select computer (under the advanced tab in Boinc Manager).
Your problems might be due to the new security in Ubuntu, so check what your access rights are to the Boinc files and folders – just grant yourself full rights if you have to. I can't remember for sure but I vaguely remember using nautilus to access the Boinc folder and then set security rights. My linux skills are limited and I'm not presently using any version.