How can I get my radio and windshield wipers to come on when I turn the engine on?

So here's the problem, my radio and windshield wipers only turn on when I have the car in
"Battery Only" mode. When I turn the engine on, and the car is fully running, neither of
them work, yet my exterior and interior lights still do. I've tried simply restarting it, turning
it all the way on directly from "Battery Only" mode, and even giving it a jump, and yet the
problem persists, I'm in need of some serious help.