Hi again Sammy,
Oh yeah, very nice pics! It's nice to be able to see the entire circuit now as that helps a lot in trying to figure out what is going wrong.
After looking at the pic's I sill have to agree with the other poster's here in that the dead or near dead pack is causing the problem.
However, we can still adapt the power resistor to take the full charger voltage if you like.
The power resistor limits the current to the pack, and the smaller resistor limits current to the LED who's brightness varies a bit with the charge current level.
The pack voltage is 14.4v as you indicated, and the wall wart is 19v that can handle 500ma, but we'll start with a design for 250ma which is a nice comfortable charge level.
We start by taking 19 and subtracting 14.4, and that gives us 4.6 volts. That's the voltage that the resistor has to drop when the cells are just starting to charge.
The resistor value will be 4.6/0.250 which comes out to 18.4, so we'll round up to 20 ohms for now. Now the power is 4.6/20 which is only around 1 watt, but that is when the pack is working perfectly which we are going to assume isnt always the case. With a pack voltage of zero volts, the power can be as high as 19*19/20, which is close to 18 watts.
That means we would really have to use a power resistor able to handle at least 30 watts, and that means at least three common 10 watt resistors in series or three in parallel. Lets say we use four in series, that would mean four 5 ohm resistors, each rated for 10 watts, which would give us 40 watts which would definitely handle the required power. The charge current near the end of charge will be lower however.
Now to calculate the other resistor. Since the voltage can be anywhere between 19 volts and 4.6 volts, we really have to use a 1k ohm 1/2 watt resistor. The LED may be a little dim near the end of charge, so you may want to use a high brightness LED rather than a regular LED, and it should be Red.
Note also that you will have to mount the power resistors where they can get free air flow too. This might mean mounting them outside of the charger case. For testing, you can wire them up and let them hang from something and see how hot they get while charging a dead pack.
I do have to caution you however in that if the pack voltage is that low then you should really fix it before charging. That's the best way to do this.