Precision 3510 laptop will not power up:  Pressing the power button does nothing. It was working just hours earlier.

Tried with no charger, and with charger.
Tried with no battery (charger only).
Tried alternate charger (known working).
Pressed and held power button with no battery and no charger for over 30 secs, then reapplied power. 
Removed battery and charger and let sit overnight.

All to no avail.

With the bottom cover off I can tell the heat sink is getting quite hot - hotter than I think is normal (but not sure).

Is there anything else I should try?

 

 

Thanks.