Hi scott94
your PC will still be under warranty but under UK consumer law the responsibility for this is now with the manufacturer Packard bell as you have had the pc for more than six months. as it has never worked correctly I would Write to Packard bell or at least e-mail them
Contact link and explain your problems. explain that you need this pc for university and give them an actual date.
Unfortunately, as Bassfisher said, intermittent faults are the hardest to solve as the are not reproducible to order and thus diagnostics are difficult.
sorry can't give simple answer
but think it's important for you to get things underway with Packard bell as soon as possible.