If you really did connect the LS32 this way then I can tell you what the cause is probably.
You have one gate-input floating: gate A consists of pins 1,2 input 3 output
gate B: 4,5 input 6 output
gate C: 9,10 input 8 output
gate D: 12,13 input 11 output.

I think you made a mistake converting from 4071 to LS32

So to connect correctly:
pin 1,4,9,12 to WR
pin 2,5,10,13 to A12..A15
pin 3,6,8,11 to 374 CLK's