My white 87 NA had a stock stereo (that always forgot its presets <-- important) until about two days ago when I hooked up my new Alpine. Now, when I did this, the wire that's sposed to go straight to the battery had no voltage across it (hence the preset forgetting thing) no matter what position the key is in. The other wires appeared fine (the ACC+ wire included). Today, ACC+ - the wire that gets power when I turn the key - has no voltage across it no matter what, and the "battery" wire has a stunning 0.03V when the key is off, about 6V when the key is at ACC, and about 10-12V when the key is at ON. WTF, mate?

 

so clip those wires, run a new accessory wire to the fuse box, i.e., the fuse for your cigarette lighter for your acc. power, and run another wire straight to the battery for memory wire. simple. or if your good with wiring trace it out. thats what i had to do, turned out one of my wires was just loose at the connection at the fuse block

 

Sounds like you are on the wrong wires and have a blown fuse.

On the Alpine, the red wire should be going to the factory Blue/White. (Don't confuse with Mazda Blue/Yellow) If this wire does not have power on when the key is in the ACC position, then the AUDIO fuse is blown.

The Yellow Alpine wire should be going to the Blue/Red. If the mazda Blue/Red does not have power on it, you have a blown fuse. Do not proceed to GO until you have fixed this. If the Blue/Red does not have power on it, then you have a blown ROOM fuse. As a reminder the ROOM fuse is a 7.5 amp fuse, so if you have a high powered alpine that has a fuse of more than 7.5 amps on the alpines Yellow wire, you will need to run the Alpine yellow wire to the battery and fuse it again within 12 inches of the connection to the battery.

Black Alpine wire should be connected to the factory bolt behind the trim panel next to your right knee. IT DOES NOT HOOK UP TO ANY FACTORY WIRE. In fact if it is connected to a factory wire serious damage can occur.

If you have a factory power antenna still, the the solid blue Alpine wire goes to 85 of an aftermarket relay, while the Mazda Blue/yellow connects to the 30 of the relay, and ground connects to 87 and 86 of the aftermarket relay.

make sure those wires are correct first, way before running any new power wires. And make sure the fuses are good.