It looks like both capacitors in the pair are damaged. They're surface-mounted chip capacitors in, I would guess, the 0402 form factor (0.04 x 0.02 inch). I can't say what capacitance with any degree of certainty as it's not printed on them (actually, I've never seen it printed on a chip capacitor for some reason, unlike SMD resistors) but, if I had to pick a value out of the air, I'd say 10nF seems a sensible figure given their purpose. They're most likely used for power supply decoupling (basically, smoothing out the lumps and bumps that are introduced by high-speed logic switching) and are in parallel with all the other similar pairs (and many others all over the board adjacent to chips, etc. - it's best to do the smoothing as close as possible to where the noise is generated) so the card would almost certainly work without them - a couple missing is likely to be "within design tolerances" unless the designers are sailing very close to the wind.
Replacing (or removing) them is doable with a very steady hand and a small soldering iron; if you have access to a hot-air SMD rework tool, that may be easier (or maybe not - it could be an acquired skill). I've known people to successfully do mods on games consoles (involving similar stuff like changing/removing surface-mount components) with just a small Antex CS iron that I would have thought twice about attempting with "the proper tools".
That said, I'd have to question what other damage may have been caused by (or been the cause of, or resulted from the same fault that caused) their failure. If the card doesn't work with the two caps removed, it's probably because something else is damaged, not because they're essential to it working. The fact that they appear to have gone bang (there's evidence of smoke nearby on the board) suggests that they may have gone short-circuit and passed a large current briefly before breaking.