Starting issue

Yesterday I got to work and I accidentally left my lights on so my battery drained. I tried to jump the car and when jump would only crank and my radio won't come on even in the power position not in the starting position. I always run it this way once to oldest to listen to the radio. Now I replaced the battery it's still doing the same thing and the radio still will not come on on. My connections are kind of loose and ones kunur really rusty in my it was going to really rusty doesn't like it's getting to connection and I really can't tighten the arm leads. Do you think that is the issue?