That could also be RAM or a bad GPU. I don't see any bent pins around the RAM chips, but you might want to examine those closely. Also, it looks like someone (you?) did rework around the main power section. This board did not use through-hole electrolytic caps, just SMD cans. They're notorious for failing (mine have not -- yet). If you're any good at soldering, and particularly if you have good tools -- a heat-controlled iron and, even better, also a hot-air station -- then here's what I would do:
Remove one of those little ceramic caps like the ones you're missing, and measure them. If you don't have a capacitance meter, and aren't interested in picking one up (I like the kind that look like tweezers with an LCD), then maybe go for a middle-of-the-road 220nF as a wild guess. Those kind of look to me like 0603 size. That's 0.6mm by 0.3mm, if you want to measure. Get some replacements and repair those missing caps. It's probably not your main (or only) issue, but it's a good start.
Then, tackle the large SMD cans. Replace those with a good brand -- e.g., Panasonic, Nichicon, Rubycon. Get a part that is low-ESR, or use something like Digikey's parametric search to find the capacity, voltage, size of the one you're replacing, and choose the one with the highest ripple current rating at 1kHz. That'll make sure it's suitable for switching regulator use. Make sure to clean that area of the board thoroughly after removing the old parts -- they leak, it's partially conductive, and it corrodes the copper on the board.
If this is all way out of your league, someone may be willing to take on the repair for you. There are lots of places online that do that kind of thing, or members here might be up for a night of breathing solder fumes. Just make sure you trust them and their work before sending off a rare(ish) part.