The attached error message looks to be unrelated to the problems that specific students were having earlier. The error message in the image comes from WeBWorK being unable to contact the database, and would likely have affected all users. This is likely because the database server wasn't started when the web server came up. Either it was manually started afterward, or is set to start later in the boot sequence than the web server.
You should check with your system administrator that mysql (the database server) is set to start automatically when the server boots, and that it is set to start before apache (the web server).