So last monday it also happen to my heavily used scratched and dirty N900. I had it in my pocket and when I get it out it was off and would not switch on.
Because of a weak battery I thought maybe I got a call and due to high power consumption the phone switched off.

Symptoms:

• phone would not switch on no white led completely dead.
• connected to car charger the led constantly green. Not booting into charge mode
• tried different batteries charged in other N900 no effect still dead.
• connected usb to windows and linux system, phone was not recognized (dmesg, syslock) led stayed dark - no charging
• while connected to usb port removing the battery the led was constantly green. Putting back the battery led was still green.

Fix:

I opend the phone to look at the components if they are not loose.
I recognized lots of dirt, dust and organic mix.
Cleaning the two hot spots of dirt with ethanol and a small brush from a razor was the solution.
I marked the position in the picture below. The section under the hf shielding was so dirty that you couldn't see the electrical components.

It is still dirty and needs more cleaning. However it is already a difference like between day and night and it is working again.