Thanks for all the advice. You have convinced me not to
rush the whole thing into the kitchen oven

To answer some of your questions:

Yes, the PCB has plenty of plastic parts. But I assume
it was assembled in a reflow oven, and therefore there
must be a safe temperature range (hence my posting here).

The laptop is a subnotebook from a major manufacturer.
No need to put a black mark on a specific one - I have
read reports of spontaneous shutdowns affecting HP, Dell,
Toshiba, etc. It is a Pentium M with i801/i855 chipset.

The failure scenario probably involves mechanical stress
and vibrations. As long as I do not type on the internal
keyboard or tap on the PCB, the laptop is quite reliable;
unfortunately I still cannot locate any specific faulty
component. On the other hand, I would expect a cracked
pad to cause the laptop to hang rather than shutdown.
Or maybe these chipsets are designed to shutdown when
ECC-like errors occur ?

I have seen my share of leaking electrolytic caps, but
this board has only SMT capacitors. Is it possible to
visually recognize a blown one ?

AC