Won't start up after low battery

I work in an office with many Macs and two of them are doing this same, odd, behavior:

-computer battery went low over the weekend (about 10%)

-user closed computer without shutting down

-computer was connected to power about 30 minutes later to charge

-computer was opened this morning and would not turn on (status light is on)

-computer was connected to power and now shows a full charge by pressing the battery level indicator button (green lights)

-pressing the power button does not turn it back on (status light is on)

-pressing and holding the power button will turn it off (status light goes off)

-pressing power button again only results in the status light coming on, no other noise or activity.

I tried:

-multiple cycles of pressing power button

-power button with option key

-plugged in and not plugged in

-connected to external display

nada on all counts.