I think without specialized equipment and the full circuit schematics of the card (which the manufacturer seldom makes public), you can only identify loose connection and visually damaged components such as burned ICs or bulge capacitors. I know how to visually identify bulge through-hole capacitor (they are easy to spot). These are much more common on old ISA sound/modem/network card and seldom found on a PCI or AGP video cards, which use mostly SMD components. I think faulty SMD capacitor can only be tested using an ESR meter - but again they are too small, how to probe? And even if you could identify the faulty components, it's difficult to replace - these types of cards are not made to be repairable. When it fails, send for RMA if warranty is still valid, otherwise throw away.