You do not have to re-start the series. If you have documentation of your first vaccination, just go and get the second and third dose. Depending on your age, it would be a good idea to get the menningits (Menactra) vaccination. Also, most colleges require you to have had both your MMR shots and be up to date on your Tetanus/Diptheria booster (last 10 years). There is a new booster given to older adolescents and adults in need of a booster. It is called the Tdap which is the usual Tetanus and Diptheria vaccines but also includes the Pertussis (whooping cough) vaccine to boost your immunity to that. If you have children or are around them, its a good idea to go ahead and get this booster if its been 5 years since your last Td booster. ~Mac~
See if they can check your titers with a blood test. Maybe if it comes back that you already have some antibodies, then you could just get the last two.
I'm not a Dr., but when I returned to college as an adult some years ago, they wanted me to get a measles shot because I hadn't had one after a certain year and they wanted evidence of a shot after a certain year (which i cannot recall now). Not wanting to get another shot, I had my Dr. test my blood, which showed sufficient antibody titer level so I didn't need the shot.