Caps are used for power-supply smoothing (or "decoupling"😉. This is especially important in digital circuits where a digital device switching between states causes a sudden demand for current.
Without sufficient local power supply decoupling, this current "spike" cannot be supplied directly from the power supply due to the inductance of the connectors and so will cause a sharp drop in the power supply voltage near the switching device. This can cause other devices to malfunction resulting in hard to trace glitches.
I'd say if the Radeon is w/in warranty, RMA and grab a new one.