We all have problems with various products, and I suppose Staples are treating your problem in a normal and routine manner regarding a repair procedure. To the tech people, your uni work or travel arrangements are of very little concern, unless you have made this in a form of complaint to the manager, who you stated "was very helpful".Having a cover plan can be beneficial if the terms and condition are right, but at the same time they can have disadvantages regarding priority of fixing.The working hours and procedures are governed by company arrangements.
You do not seem to mention the age of the notebook, and whether you have had previous problems since purchase. The manager does seem to have taken interest in a quick resolution, and you will have to wait another day, after they have received information themselves.
Remember though, if a replacement is offered or a repair procedure is undertaken (as was previously), then you may lose all your work, if you do not have back-ups.Staples or the repair agents will not be held responsible for this, and no doubt this is in their terms and conditions!.
More information as to your consumer rights click here