Power and hard drive lights flash on then shut off

I’m trying to fix my parents HP Compaq nx9005 laptop.
When you press the power button, the power, and hard drive lights flash on, then shut off immediately (doesn’t even last a second). The power light will also remain off until the reset button is pressed again, or you unplug the AC adaptor, then plug it back in. Once it has been reset the power light blinks with an amber glow (with the battery out).
I’ve tried this with and without the battery. I’ve tried it without the hard drive. I’ve switched the RAM in various combinations. I’ve tried connecting the laptop directly to my desktop monitor. Same result every time. I’m guessing it’s an internal electrical problem, but I’m not very experienced with laptops as opposed to desktops. Any suggestions what to troubleshoot next? Thanks in advance!

First of all, make sure that the AC adapter is working properly. Ideally, I would try to replace the adapter with a test one but if you don’t have it at least check the voltage on your adapter. It’s not the best way to test the adapter with a multimeter. I’ve seen some failing adapters with good voltage readings. A bad AC adapter would be an easy fix for you.
Just recently I had a similar problem with Compaq nx5000 notebook. I was able to turn on the computer, but it shut down after a few seconds (your notebook shuts off immediately) and the video never appeared on the screen. I tried to troubleshoot all basic stuff, as you did. I removed the hard drive, battery, DVD drive, wireless card, replaced the memory module but nothing helped. Finally, when I was checking all internal connection, I discovered that the notebook works fine with an external monitor attached when the LCD screen is disconnected from the motherboard. By the way, this connector is located under the keyboard strip – a piece of plastic just above the keyboard. As soon as I connected the LCD cable back to the motherboard, the laptop didn’t start. So, I took the display assembly apart and found that the video cable wasn’t seated properly in the connector on the back of the screen. The problem was fixed as soon as I plugged the video cable back in.