First do a quick test of the power.
Do you have a multimeter? If not, get a tail light bulb and some wire...
Check the amp, do you have a proper ground wire to it from the battery, or the chassis?
Now check for 12V to power it, either with a multimeter check between the 12V terminal on the amp to the Ground terminal. 12V? If not, check the 12V terminal to some bare metal or a screw into the chassis. 12V now? if so, your ground is bad.
No multimeter? take a tailight bulb, and hook a short legth of wire to the two connections on it (I have a taillight bulb in its socket I ripped out of a old car just for this purpose) Check the same as above, Light=12V. Sometimes the taillight bulb is a better check than a multimeter as it puts a load on the circuit. IE, you could have 12V on the meter, but if the ground connection or power connection is bad, trying the same with the lamp won't light it as the connection can't handle any current.
OK, so we now have 12V and ground verified correct? Check the Amps fuse. is it good? Now lets check the amp. take a short length of wire, and connect it to the remote terminal. touch this to the 12V Terminal. Does the amp power up/click/light up? if so, your amp is fine. Take your multimeter (don't use the bulb here too much load) and turn on your deck. At the end of the remote wire near the amp, do you have 12V between the remote wire and ground? If so, you should be good to go, if not, check for a inline fiuse on the remote cable, check right at the deck remote out for 12V when the deck is on. If not the deck may be bad....
Now before we rule out the deck, quick question..... (I love this one cause i've smacked my head so many times before with it in the past). Is this a factory deck? If so, (or if its a cheaper deck) is the "remote" wire your tying off called "remote" or "Antenna"? Many decks, escpecially older ones may have an antenna out, as well as a remote out. The difference being, that the "Antenna" power wire ONLY has 12V when the radio is on AM or FM to extend the power antenna. When in Tape or CD modes, the line is dead. I had a guy I did a install for when I first started like 14 years ago, I did a nice install, hooked up and tested everything. And the next day he brought it back, every time he put in a tape (CD's wern't big then) the system would go dead..... Took me a while to figure it out, I thought the deck was bad, but there were two connections on it, one for antenna, and one for remote.
Good Luck! Let me know if this helps!
SD