Diagnosis of the fault would be quite quick especially as the faulty capacitor is usually visually obvious.
The capacitors in question are typically 10mm diam x 15mm long and are used in the switchmode buck regulators (the ones near the little toroidal coils) and for general power filtering at regulator frequency (surrounding the cpu and scatteded over the board. They are usually throughhole components in the hundreds and thousands uF range. The other capacitors on the board are mostly high and very high frequency power supply filter ceramic surface mount capacitors in the nF range.
As failure of one would lead to the suspicion they were all dubious any proper repair would involve replacement of them all - typically ~ 30.