Please don't take offense at this, but the situation you are describing would appear to be almost impossible - the only time power is not directed to the rear wheels is when the transfer case selector is in the N position.
You haven't mentioned any problems in 2H, so I'm going to assume that there are none - if the vehicle moves in 2H, it's also going to move in 4H - the difference between the two is that the front output hub has been engaged, nothing changes with respect to the rear output shaft. Selecting 4L engages a reduction gear system and drives the rear output shaft, which is still coupled to the front so power is again sent to both axles.
A couple of questions to try to narrow things down ...
What type of transmission do you have - manual or automatic?
What condition is the engine in?
How steep is the hill?
In theory, if the hill is steep enough, and the engine tired enough, or there is slip in the transmission, you might not be able to get enough power to the wheels to climb the hill, and the additional torque multiplication of the low range allows the vehicle to move.
By the way - there is no "vacuum" involved in the 4WD system on the Grand Vitaras - it uses positive pressure (vacuum would be negative pressure), and all it does is engage the front axle freewheel system, all the 4WD selection is mechanically handled in the transfer case