MySql database upgrade

Hi, I am revisiting an old project that has been neglected. www.mycarsupermarket.co.uk was built 5 years ago with the data base on an old version of MySQL (4.?) It has been transferred to a new server and MySQL client version: 5.0.95

Everything works ok except admin cant log into the back end and users cant log into there profiles or register new

Initially I am looking for someone who can fix this problem