Sounds like something going on at the fuse box, as radio, backup lights, and blower motor/AC are powered by ACC and fused by 2 fuses. Might be a bad ignition switch or bad/nearly broken wire for ACC at fuse box. Usually, it is the BAT line that breaks, not the ACC line. Something is going on that when more power is pulled through those lines, continuity is lost due to higher resistance. I'd check your fuse clips first.