Whoa, whoa. Your cd player ended up cutting out on a duty cycle-type trigger, to avoid damaging itself. That, or the subs are too low of an ohm rating for your deck.
Never believe what the CD players say on them for what their power output is. There's no regulation for what they are allowed to print. They could write 1000x6, and it would fly. Truth is, they rarely put out more than 15 watts per channel. 45x4 really means, you MAYBE get 45 watts, at max volume, with the deck rounded down to one channel. It's a load of crap. What you really want to look for in a deck is a good amp preout voltage.
The remote wire is triggered power. It's any power source that comes on with the ignition. If you have an aftermarket head unit, it will be the blue wire, or blue with a white stripe. If you do not have an aftermarket head, then just check for fuses that get power with key on.
Make sure you get a nice ground set up in the back, or it will make a lovely POP when you turn it on.