As you can see below 
, this cap is marked 8 + 8 uf. Does this indicate that it is a dual cap? There only seem to be two actual terminals, as you can see here 
, although there are also three lugs around the rim. Can anyone help me understand what this component is and what the terminals are?
Is this a dual cap
capacitordual
Related Solutions
Process of elimination/deduction
Always start with what you know.
(i) There are three components in the circuit - resistor, diode & capacitor.
(ii) There are three terminals (A,B,C)
(iii) There is only one component connected between each terminal.
There are only two possible unique configurations of this circuit.
(i) Either the anode of the diode is connected to the end of the resistor (and the cathode to the end of the capacitor)
(ii) Or the Cathode of the diode is connected to the end of the resistor (and the anode to the end of the capacitor)
Between any TWO TERMINALS you will have a circuit consisting of the 'component' which is connected to the other two component connected in series with each other and parallel to the component.
By using DC to test the components you (should) know that;
(i) the resistor will conduct the same amount of current in both directions AND the capacitor in the parallel path (once charged) will prevent current flowing through the diode regardless of polarity
(ii) the diode will appear as a short circuit in one direction only AND the (charged) capacitor will prevent current flowing in the RC parallel circuit.
(iii) Applying the test across the capacitor only the parallel circuit (resistor/diode) will conduct (- in one direction it will give the same (or similar) reading as the resistor, in the opposite direction it will show an open circuit (no current).)
Its now down to you to work out which terminal is A, which B and which C and which way around is the diode connected. For extra credit you could also calculate the value of the resistor in ohms.
It looks like your fried cap is connected right next to the input terminals of the +12 V rail and GND. Here are the steps I would try to get the drive running again:
Remove the cap. Power the hard drive, chances are it will work anyway because the cap just acts as a small filter for the incoming +12 V rail and the slightly increased ripple voltage on this rail will likely be tolerated by the rest of the hard drive. This test will also tell you if anything else has failed along with the cap or if you're lucky and the cap is the only bad part.
If step 1 was unsuccessful, you can put pretty much any cap with at least the same capacitance and at least the same voltage in place of the fried cap. Maybe the drive will work now? If you just need the drive to recover the data, any half-decent electrolytic (including tantalum) capacitor will likely do the job long enough until you finally scrap the drive. Don't worry too much about the ESR. As the cap appears to be just in parallel to the 12 V input, it's not worth counting every milliohm. However, your're of course right: The smaller the ESR, the better.
However, by the looks of it, the drive is so old that you value not only the data but the cool vintage hardware itself. Here's what I would do for a good, permanent repair: Sizes of SMD tantalum capacitors are standardized. Yours appears to be one of the bigger ones (C?, D?). Try finding a replacement cap with the same size and capacitance, and you're very right about the voltage - 25 V or more is a very good idea. There is a huge derating to be considered when using tantalum capacitors, and using a cap with twice the voltage it is subjected to in your application is not a bad idea at all. One last hint: While aluminium electrolytic caps have the mark ("bar") on the negative end, tantalum capacitors are marked on the "+" end!
As we're aleready talking about derating and fried tantalum caps: Besides (even very short) voltage spikes causing tantalum caps to fail catastrophically, they are also very sensitive to current spikes (as they will appear when you hot-plug the power connector into the drive). If you have the space, using an aluminium electrolytic cap as a replacement will be more robust. If you want to go for a "good as original" vintage repair, try to stay away from hot-plugging your drive.
Example random size chart (it gets more confusing when you consider not only the length and the width, but also the height):
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Best Answer
Yes, it is a dual capacitor. One of the terminals is common between the two capacitors in the package. The case acts as the third terminal, but you will need to see the capacitor datasheet to find out which terminals are connected to which capacitors.