I don't believ you'd get a low power icon, as I think that that's displayed by the player software, which you haven't yet gotten to when the no-disk message shows up. My guess as to what's happening is that the drive is trying to draw more current than it can get in your car and is failing to start properly.

Assuming that I'm right (and I'm not guaranteeing that I am in any way), I'd guess that the way to fix it would be to find out why it can't get that much power. The obvious answer is that your battery or alternator can't handle it, but I don't know if that makes sense (1A doesn't seem like that much). Have you tried not plugging your empeg into the dash until well after the car has started, so as to not have the ignition and empeg both putting big loads on the electrical system at the same time? Or there might be a problem with your wiring, maybe. I'd guess trying heavier gauge wires for the power and ground might help.

Please note that I'm just guessing; I'm not an electrical expert by any means.