That is an electrolytic capacitor. A 1,000 uF @ 35 volts to be exact. It looks like the leads (the wires coming out of the bottom) might have come straight off, so it might be possible, but it depends on how the other side of the board looks.
An important thing to pay attention to with these capacitors is that they are polarized, i.e. they have a particular direction they have to be installed. In the picture of the cap, you can see the black strip going down the side with minus signs on it. The lead closest to this side is the negative, while the other is positive. On the board where it came off, you can see that one side has a plus sign on it, right next to the other capacitor. It needs to be installed with the plus lead going to that hole, while the negative lead going to the other hole.