Quick power troubleshooting question

I'm dealing with an Acer Aspire One AO722 netbook and am trying to determine if the battery is bad, the external power supply (PSU) is bad or the netbook is bad.

The netbook is about 2 to 3 years old.  After sitting idle for several months I powered it up yesterday with the PSU attached. It booted fine. I left it running, probably downloading and installing Windows 7 updates. I returned late in the day and it was powered off.  It will not boot or even power p.

Symptoms:

I've measured the output of the PSU with a Fluke VTVM and it's outputing 19.5 V DC.

With the PSU plugged in and the battery installed, when I press the power button the small blue LED "lightbulb-icon" that indicates "power status" blinks 5 times. That pattern must mean something!

With the PSU plugged in but the battery removed, when I press the power button that LED does nothing. In fact, unlike most laptops, on this netbook no indicator lights up when the PSU is plugged in, whether to indicate charging or just to indicate the presence of a power supply.  I don't know what is "normal" for this network.

I fully disassembled the netbook and checked the PSU jack and it and its connection to the PCB looks fine.

I wonder if the battery could've died and somehow be in some sort of shorted state that prevents the PSU from working. Does anyone know if this netbook should work with only the PSU connected -- no battery present?

Would you agree that if the PSU is outputting the proper voltage, and if the netbook should work with only the PSU connected (no battery), that the netbook itself is broken in some way? The only symptom that gives hope otherwise is the 5-blink indication with battery and PSU attached -- like that means something signficant.

Thanks!