need helps in coding...

When you have a look at this section:

else
  if (pwm_inches > "000") then
    pwm_distance_i <= pwm_inches;
  end if;
  pwm_count := 0;
  pwm_inches <= "000";
end if;

The pwm_inches is reset at 000 as soon as the PWM pulse ends. You probably won't see anything on the output because of that. I think that your second process should use the pwm_distance_i signal instead, that should keep the value of the measured distance after the PWM pulse ends:

process(pwm_distance_i )
begin
  case pwm_distance_i is
    when "000"=>

And also in that last process, you assign led to 1 in the others section, but never to 0. If you want the led signal to be 0 when you have a valid measured distance, you can assign a default value before the case:

process(pwm_distance_i )
begin
  led <= '0';
  case pwm_distance_i is
    when "000"=>