Dell d600 power issues

The problem is in either the power lead from your powerpack or in the connector on the motherboard itself.
In this case I would say it's in the powerpack.

Dell use a smart power supply system that talks to the laptop to say if it is a genuine part or not.

If you look at the plug you will notice something strange about it.
There are actually 3 layers in there (well sort of)
You have the outer layer, then inside you will see a pin. There is another layer that is wrapping around the inside of the plug that is a mirror of the outer layer.

The wire that connects to the centre pin is not power, but the smart pin. The wire can easily break off that pin and just sit inside the cable.

Try it with a known good adaptor, or just get another one.