Charge light on if display cable disconnected from motherboard

I have a HP DM4-1050ea laptop, which recently started to not turn on either with battery alone or AC alone (with and without battery). I cannot boot with battery alone because it's drained and don't have any other means to charge it. I had done the usual troubleshooting methods like:

Booting without HDD and RAM.
Press and hold the power button.
Trying a different power cable.

But tonight I decided to take it apart. I got access to the motherboard. I managed to get the charge light to light up when I disconnected the display adapter. At this point, RAM, HDD, optical drive and keyboard have been removed.

But I'm not sure what this diagnosis is telling me. If the display cable is plugged in, I can hear a high pitched tick noise, my best guess is that it's a short circuit. What are my options to fix this? Replace the motherboard?

This is the maintenance manual: http://h10032.www1.hp.com/ctg/Manual/c03106715

I managed to disassemble the screen today so I could disconnect the display cable. The laptop booted up fine without the display cable connected, But it fails to power up if the display cable is connected, even if its not connected to the display itself.

Try another display cable??