hmm, well looking at all the stereo stuff you have on your x i feel kinda like i can assume you know what your doing and you wired everything up right. if that is the case, it sounds to me like you got a bad amp and you need to exchange it for another one.
on the other hand, i dont know what you do and dont know so here is a list of bs thats probably not wrong but you can check just to piss yourself off enough and waste enough time for you to rip that amp out, box it back up and take it back.
grounds, from the amp to the body, from the power cell to the body, from the body to the engine/battery.
leads......if a lead was bad you would blow a fuse/have no power or catch on fire......probably not an issue.
rca's.... did you use good ones? probably. can they be bad? yes. would they ever make the amp itself make noise.....not as far as i know but its possible. easily tested: disconnect them while the amp is making the noise and see what happens
your subs, you're 100% sure they're set up right? 4 4 ohm coils in parallel is a 1 ohm load, that amp is cool with that?
also easily tested, disconnect them and see if the noise stops.
break in period......brand new amp was workin just fine when you turned it on.....then did you crank it all the way up? if the problem started after that you may have done some minor internal damage to the amp. but its cool, rockford dont know that and i wont tell em

send it back and get another one. i would think if any of these new amps really needed to be properly broken in that one as powerful as yours would need it most. of course some people dont believe in break in periods tho. you can make up your own mind on that one.
back to the battery for a second here, just to be sure.....you didnt by any chance wire your battery in series did you? as in, positive comes from the front battery to the back and you hook it up to the neg of the power cell, then from the positive on the power cell to the amp? that would be bad
if the noise started after connecting the subs sounds like thats where you should start this investigation. if disconnecting the subs stops the noise you should remove the subs from your enclosure and double check you didnt cross wire anything or accidently hook a positive to a ground or something. and yes, you could have miswired the subs and they would still work well enough to make you think nothing is wrong.