The battery is brand new and charged, it is one of those normal black bricks. I just bought it for testing, since the Cyclon are crazy expensive.

I did a visual inspection of the board, but I didn't find any broken trace or via (with a light under the board).

The battery bay switch is also good. I made another cable from a dead ATX power supply and connected both of the wires to the battery and it still shows the same issues.

Which connections should I check?

Also, what is the purpose of the tantalum capacitor on the Hybrid module? when I was repairing another board I replaced it, and that brought the machine back to life.