My son has recently bought a second-hand 9800 Pro (Saphire) but his PC
"burn-out" when he installed it. The PC refused to boot and there was a
burning smell. He immediately switched-off.
It sounds to me like he has burnt-out his power supply (a cheap 300W model
which came with the (cheap) PC case).
Is that possible?
Yes it's possible, and the most likely primary failure.
Could he have damaged his graphics card?
Yes, above I wrote "primary failure" because when a power
supply dies it might take other parts to the grave with it
if it's badly enough designed. "Usually" it's just the
power supply but it certainly is possible that the
motherboard or video card and/or more are damaged... you can
only try a new power supply and see.
Will a new power supply solve the problem?
Assuming that's the problem, yes.
If you have a multimeter you might take voltage readings of
the old power supply, with it's PS_On line shorted to
ground, hooked up to a small load like an old hard drive but
nothing else, not the rest of the system, and it should turn
on and run. Even so a generic comes-with-case power supply
is not typically suitable for a system with a 98000 Pro in
it... I'd advise replacing the power supply even if the
machine were working OK right now.
If so, what rating should be buy?
Good ballpark would be 380W or higher in a name-brand like
Sparkle/Fortron, Delta, Antec Truepower, Thermaltake. There
are of course other components to consider too, but since no
mention was made of them I"ll assume they're typical,
nothing out of the ordinary and so there is no call for a
particularly high-capacity power supply like a 500W+, unless
you just wanted a better margin and more support for future
upgradability.