Planting Corn -- will it grow?

I nave planted about a fourth of my 1/4 acre in sweet corn. We'll see how it will do. I did not do much soil preparation -- just the original plowing and two times over with the tractor rototiller and then once with the hand tiller. I made long furrows with the hoe and then spread the seeds by hand. I planted approximately 4 inches apart and covered with about half an inch of soil. That's a bit close for corn, but I don't expect to get a very high germination rate in this grassy soil, and seed is cheap.
The problem I see is clearly visible in the picture: lots of competition from the abundant grass rhizomes. It seems that the soil here is mostly grass roots. Those thick rhizomes will grow new grass stems and it won't take long. The challenge this year is to kill enough of the grass to let the corn crow. Time will tell.
The early corn I planted 3 weeks ago did not germinate. I dug among the rows and found un-germinated corn seeds. The seed was given to me free and it was probably last year's seed. it lost its vitality over the year.