computer power supply unit is the best option, short of having a car battery in your house. to find out how to do it just search it on youtube, thats how i found out.
you basically have to put 14th and 15th pin connectors together (from the motherboard, usually the only green wire and the black one next to it), this will enable the PSU to turn on.
then get your amp and run ALL the 12v rails (yellow) to the amp, i say all because multiple wires act like a better gauge cable. then loop a sall piece of wire from the batt. on the amp to the remote. then ground ur amp.
as for the headunit, you will need one 12v rail from your PSU and connect it to your 12V (yellow again) and the ACC (accessory, which is red) on your headunit. it should now power up. then connect your speakers using the (on mine are) purple, green, white and grey wires, they are in pairs. if you dont understand then once again look on youtube.
hope this helps you, just make sure that your PSU is powerful enough like jsnyder88 said.
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computer power supply, very cheap to buy, i am currently using one to power my car stereo and amplifier in my house, just make sure you get one that is at least almost as powerful as the amount of watts you want to run, get one with a power switch on it if you can because some dont have one
http://www.audiokarma.org/forums/showthread.php?t=187730Short story, it looks like the electronics to convert house power AC to car-like DC power is costly and you have to know what you are doing. It may be easy to convert just the tuner or CD player but you are looking to move the "boombox" setup out of the car which may not be cost effective.