I assume you have it fused?
1kw rms can draw well over 100 amps for a decent bass thump.. Keep in mind the stock alternator doesn't generate that much juice, let alone at idle. just for kicks, hook up a volt meter, and watch your battery voltage with the radio cranked up (after you figure why it is not working).
If the voltage drops much below 13 with the engine running, you gave issues. I would also put in a "super cap" to help absorb the power spikes the amp will be causing. Put the cap as close as possible to the amp, and follow the instructions for precharging it before you hook it into the power system. They also fraw well over 100 amps if you hook them up "cold" (as in discharged) You need to "warm them up" (has nothing to do with temp, more that you didn't pull it out of the package, and shove it in the truck) with about a 1 ohm resister, 20watt range, and hold it with pliers, till the voltage is within 500 to 1000mv is your battery voltage. if the fuse ever blows, or you disconnect the battery, you have to precharge the cap again, or spend a hundred dollars on fuses, till it charges itself.