2006 I-280. Why does A/C blow cold air only on high speed?

Check fuse first
then scan PCM , oops you didnt and the BCM does run this stuff.
so not scanning it , you miss all those FACTS.

the blower is dead. (aka , not spinning , or silent)
on all cars made the answer is the same.
blown fuse, fuse marked BLower, is blown. LOL.
controls not turning it on, controls failure.
blower bad. (motor) hot wire it in place to test)
wires to any of the above.
or the resistor block bad, (if it works on high but not low)
i have the schmematic in hand.

the HVAC relay pulls in by command of the BCM
the relay then sends 12vdc power to the blower via fuse 41
the blower is now hot full time.
the blower then needs a ground to spin (run)
on high, the ground G601 via the speed knob,switch makes that ground connection, so if the fan dont spin and say the fan is ok
then the relay is not closing or the fuse 41 is blown. (why not look at the fuse first for all electric fails)
the BCM sees you, turn fan on, (heat or cold)
and closes this relay, on the left.
if the relay does not close, (and coil is ok inside)
the the BCM didnt see those HVAC requests.
use a scan tool and look for BCM errors..>??????