The lamp base is where the light bulb goes in,
Have a look inside it, there should be two metal contacts.
If you can safely put your ac volt meter probs on them,
this will tell you if the power is making it that far or not.
Heres what it can be-
1 - Faulty lamp base.
2 - Wire from lamp base to ceiling faulty.
3 - Loose connections in j box.
Work backwards with voltmeter to find faulty part.
If theres power in lamp base, its faulty and probably not making good
contact with lamps.
If no power, next to check is j box, put volt meter on wires,
If power there ok, then no power at lamp base,
cord is faulty.
If no power in j box, check connections for loose
or wrong placement.
That counterweight would put some strain on the cable,
and the pulley would bend the cable.
So my guess is its the cable thats faulty.
But check everything anyway.