Here is my guess:
The capacitor is a power supply filter capacitor, the purpose of which is to take noise off the DC power on board. Chips perform most reliably with a completely noise free power source. Unfortunately the chips themselves put noise on the power supply as the transistors switch on and off.
In fact, being next to a diode (black cylinder) and a voltage regulator (square thing), this capacitor is probably part of a circuit to supply a reduced voltage to the card. Good engineering practice would have a capacitor at the input side (the one that is missing I think) and output side of the regulator, but in real life it probably works without it under most circumstances. I don't think it would hurt to try it as is.
If all you've got is an old part with too short leads, what you can do is solder some leads (cut from a resistor perhaps) onto the short leads.
The way we always replaced parts at the factory was to get the solder out of the holes first. We used custom made, extra strong solder suckers. The solder suckers you normally get at an electronics parts place are weak. A solder sucker has a tube attached to a rubber bulb you squeeze and let go to make suction. You melt the solder with your iron in one hand and then get the sucker on the pad as fast as possible before the solder freezes. Without a solder sucker, possibly putting something that solder does not stick to in the hole while the solder is melted will clear the hole. Maybe the tip of a pin or safety pin. To make the solder melt easier, we always melted some new solder on the solder pad/hole first. The difference is amazing. (Probably this works because the solder sold for electronic repairs melts at a lower temperature than what they use in mass production.)