That's a capacitor (well i think it is, because it seems to say 'C5' next to it). It seems to be just connected in series with the other capacitor 'C6' across the output, for interference suppression OR it's part of the Class-D lowpass filtering (Class-D's by design make high frequency noise). Should not be hard or expensive to replace (cap is worth 10cents max) once you get the value of it - if C6 has a value printed on it there's a good chance C5 is the same. It would probably run fine without it, just means you are sending some high frequency (probably >20Khz) noise to the speaker. Since it's a sub, you aren't going to hear it anyway, just keep the sub's speaker cable away from any other cables so it doesn't induce high frequency noise in your other speakers.
Your guess is as good as mine as to why it failed, hopefully it was just a faulty part and not caused by another fault in the amp. I'd be asking for at least a partial refund on the basis that it failed because of abuse.
Edit: the terminals are electrically connected (the amp only has 1 output, with 2 pairs of terminals for convenience), so it doesn't matter which terminals you use as long as the sub is connected to a positive and a negative
Edited by TMM, 17 June 2012 - 04:08 AM.