I have a model #pr675nrvt "STATE SELECT" gas hot water heater, whose power vent blower fan runs continuously.
Does anyone have a solution to this problem ?

The power vent has a temperature sensor that starts the blower. Some units use and anticipator that starts the blower prior to firing the gas flame. This is what is failing on your blower. Blowers are not difficult to replace and may be cheaper than paying someone to fix your current blower. Check the internet and plumbing supply houses for a better price.

It is a sticking relay in the control board.

Thanks northern heat, I had same problem and tapped on control and blower unit stopped. (temp. solution)