i would say if its not a bad relay a new blower would probably fix it - maybe something internal is corroded and causing it to think it should be on all the time - if you're super handy you might be able to take it apart and dissect it to see if anything looks wrong
i think there are some kind of resistor coils that can break off and/or attach to a different part of the coil to complete a circuit - but dont quote me on that