radiator - does it stay on the whole time the key is out of the ignition or does it shut off after about 5-10 minutes? some car has it to where it cools the motor down a little bit than it'll shut off - if it doesn't shut off than the fan is hard wire to your battery

speedometer - cheeck your vehicle speed sensor on the tranny.. it might be a bad speed sensor

give us more info on your vehicle - make, model, year, etc.