To understand the old slave song you first have to understand that the South, especially inland like Georgia have traditionally been a place where people starved to death a lot.
There is a nutritional deficiency called pellagra that is still rather
common, does weird things to the thought processes. You also have to consider the last line of the song, "Cuz the master's gone away", then it all makes sense.
For a lot of slaves corn was the only thing around to eat, and it was usually dried, not fresh, tasted like crap and gave you a weak brain.
"Jimmy" is a corruption of "gimme," so the song essentially means "I would be willing to eat something as vile as cracked corn and I'd still be happy (don't care) if only I weren't a slave (master gone away).