How are people suppose to tell you why a circuit isn't working if all
that you tell us is that it's not working? For all we know, the circuit
could be working perfectly and you don't recognize it as such.
Are you sure of your wiring and it actually matching the circuit
diagram you've given?
One thing is for certain, you're powering the circuit with 5v yet
you're expecting it to react to an imput signal of upto 5v..
All examples in the datasheet show a maximum input at least
1.2-1.5v below V+.
Not sure why you have 5v on pins (REFout & Rhi on the bottom 3419)
that's tied to ground (i.e. 0-volts normally). Certainly no 5-volts there
according to your diagram. And the original circuit (per page 8)
shows at least one resistor between those pins and ground.
Grounding the REFout puts zero volts across the resistor divider
network (in the chip itself) so there's no way any LEDs could ever
turn on. Since REFout is actually a voltage output from within the
chip, you may have damaged at least one of your 3419's by shorting
this output to ground. Again, all examples in the datasheet have at
least one resistor between this pin and ground.
How 'bout if you build the 20-LED circuit on page 15, for a signal
between 0->2.4v, and get it working before trying to modify it for
your own needs?? Start by building a circuit that's known to work
to understand some of the concepts then move on to modifications.