if it's making a loud clicking sound, that's the starter solenoid try to engage, but it can't, because it's either a) broken or b) doesn't have enough juice. probably the latter.
you may have an existing issue that the stereo is exacerbating. or it could be completely unrelated- cars do weird things. i would make sure battery terminals and starter connections are clean and tight, and check the voltage at the starter b+ terminal while cranking. if it's low, check voltage drop across the starter cables while cranking. you place one meter lead at one end of the cable, and another at the other end. the meter reads the amount of voltage difference between those two points. if the cable or connection is bad (and the battery is good) you will seeing a higher than normal drop in voltage across the cable. anything more than maybe half a volt is definitely a problem. check between the battery positive terminal and starter b+ terminal, the battery negative and the chassis, and the chassis and the engine.