Your car has the small 8 - pin connector and the radio you are trying to put in has the big quadlock connector, right?!?! If so, you've got a lot of work ahead of you and it is simply not worth the effort.
The '04 looks for illumination, "s-contact" (key-out), speed-sensitive (gala) all over can-bus, and your car won't have that signal coming in.
I'm 99% sure that the radios started to get CAN in 2002, not 2001.
For your particular issue, it SOUNDS like you have the yellow/red wire hooked up to the new radio, and you should NOT. You should have both Red/White wires hooked up to the two power inputs, and just tape off the end of the yellow/red wire REALLY WELL because it gets 12V while the ignition is on.
That won't solve the other issues though...
Cheers,
-Chris