Student house, problem with cooker?

A gas cooker would not fail the test just because it's dirty, the burn marks occur overtime with use on a grill and is probably just the grease from cooking. If you can't turn on the grill or hob burners at all this would fail the test. The ignition should be repaired. Your lettings agents should of given you a copy of the up to date safety certificate when you rented the place.