Well I'm glad to see that you are moving forward with database's, single table database are nothing more than flat files with an SQL interface.
I'm not sure that I understand your problem, but from what you have I'll try to put something together.
First off you will have a list of all of your faculity members in the faculty table. When one of them enters a trouble ticket you will just put there unique id into the requested by table. This way when a staff member looks at the trouble ticket you can query the faculty table and get the information on the submitter of the ticket. This lets you keep only 1 copy of redundant data, and referance it with your unique id's. Now when the staff member does something to the trouble ticket then you will put his id on the ticket, so that when the facuilty member comes back to check on it you can pull up the staff members information.
You will probably want to have another table called status that holds all of your status' and then just put the ID into the ticket table.
Also you might want to have a notes table that will allow the staff or faculty member can write up a description of the problem, or the solution. Then you'd link these notes to the ticket with what is called a cross-referance table.
notes
id
submitted_by
submitted_type - either staff, or faculty so you know where to look for the above id.
note
tickets_x_notes
id
ticket_id
note_id
Using this you can link any number of notes to a ticket. Ofcourse this is a simplified table structure, you'd probably want to add thinks like date/time...
Anyway the main reason to normalize is so that you can minimize the amount of data that you are storing, and give yourself access to that data when it is needed through a speedy method (unique id's with indexes).
I hope this helps, let me know if you need anymore information.