http://www.imagehosting.com/out.php/i505146_back1.JPG
What you see on the back of the card there, is two switching
power converters (upper left and lower left). One perhaps used
by the GPU, the other by the video memory. The transistor
that burned is a MOSFET. Since the MOSFET failed, the output
voltage of the switching power converter could have been
incorrect (too high or too low) while the thing was frying.
So, while you can look at the part number on the device, go
to Digikey or Mouser.com and get a replacement, solder it in
place, the card still might not function when you are finished.
And there may be a second component, that pushed the MOSFET over
the edge. If you don't find what caused the failure, the
replacement MOSFET might go exactly the same way, on the
first try. (Note - check the condition of the contacts on
the edge of the card as well, as they might have got burned
too.)
To see a typical circuit for a switching converter, this is the
schematic for the Vcore converter on a Gforce2 card. The
controller chip is a US3007. Q3 and Q4 on the right are
MOSFETs. If Q3 fails shorted, Vout1 rises higher than normal.
If Q4 fails shorted, Vout1 drops to lower than normal. And
the burned transistor can be the one that is *not* failed,
as the failed one, puts the stress on the other one, as long
as the gate drive is still there. So it could very well be
that the one not burned, is the one failed, and the burned
one is the victim. (I.e. Replace both.)
http://www.xbitlabs.com/images/video/geforce2-overclocking/us3007-typ.gif
http://www.xbitlabs.com/articles/video/display/geforce2-overclocking.html
The gate drives on the two MOSFETs alternate. They take turns.
When one fails shorted, the other MOSFET might still be functional
and continue to switch. Each time it switches, the whole rail is
dropped across the switched on transistor, which is what causes
it to burn. If the controller chip detected a problem, it would be
able to disable both gate drives. But not all faults will be
successfully detected, which is why it might still burn.
Tracking down the controller chip part number, may lead you
to a datasheet for the chip, with a description of how it works.
This is the sheet for the US3007, but the chips used on your
video card won't be the same as this. (The search engine used is
datasheetcatalog.com)
http://www.ortodoxism.ro/datasheets/unisem/US3007.pdf
If it was the GPU that failed, and started drawing too much
current, then some controller chips can detect that. Which
would result in the video card no longer functioning, but
no burned MOSFET. Since you have a burned MOSFET, the source
of the trouble could well be the MOSFETs themselves.
And I'm not going to quote you odds, on what shape the GPU
is in right now. There is no way to know for sure. As for
the practicality of repairing it, this is most likely to
only be practical if a hobbyist tries to fix it. The labor
charge of a professional, would make a new card a cheaper
alternative. MOSFETs are reasonably cheap, at a few bucks
each.
Good luck,
Paul