Difference in total pressure when HVAC system is on or off
If you are measuring the pressure inside the duct, before the diffuser, the pressure should be detectable.  The velocity pressure is given by Pv = pV^2/2 where Pv is velocity pressure, p is the density and V is the gas velocity.  

Taking a wild guess at a velocity of 5 m/s, gas density of 1.29 kg/m3, then Pv = 16 Pa

The static pressure should be equal to the pressure loss across the diffuser, which may not be very large, but is probably in the range of 5 - 10 Pa.  

I would suspect your problem is one or both of two:


The BMP180 is a barometric pressure sensor, and is designed to measure pressures on the order of 900 - 1000 mbar, you are asking it to detect a change of about 0.25 mbar, which is very much at the limit of its accuracy (regardless of how it's advertised).  Moreover, the electronics to which it is connected will add error to its measurement as well.  Static and total pressures in a duct are typically measured using a differential manometer, comparing the pressure inside the duct to the pressure outside the duct, because this is a much smaller number and allows a much more sensitive instrument.  Velocity pressure is usually measured by comparing the static pressure and the total pressure inside the duct.  
Placing a flat pressure sensor (presumably mounted on a circuit board) into an airstream will likely not yield the stagnation pressure of the gas in the airstream at the aperture.  The sensor and the circuit board will so dramatically disturb the gas flow as to change the direction and likely create a point of 0 velocity at the pressure sensor.  Total pressure measurements are taken using pitot tubes which are carefully designed so that they will allow the gas to flow around them with minimal disturbance and collect the stagnation pressure at the aperture.  Once again, I think the BMP180 is the wrong instrument.  


If you aren't too concerned about accuracy, you can make a makeshift pitot tube out of a piece of copper tubing bent so that the tip will point into the gas stream.  The more aerodynamic the tip, the better.  I wouldn't use this for spec'ing a $100,000 fan, but for fun around the house, it might be enlightening.  

As far as the manometer, you may try using a tube, folded in a U-shape and taped to a ruler marked in millimeters, and filled halfway with water.  This will still just barely register at the small pressures you're looking at.  YOu can experiment with changing the angle of it to make it more sensitive.  The greater the slope, the more the water will move in response to a given pressure.