Give it a chance. Most turf grass"s will go dormant, turn brown and just lay there until conditions improve. My yard looked the color of a McDonalds french fry until we had 2"+ inches of rain over 48 hours last week. It"s not "spring green" yet, but it looks entirely different now. We were bone dry since mid April.
I do have one patch of grass that lays over an old abandon septic tank. That grass died due to excessive heat that apparently built up during a 12 day stretch where we saw daytime highs stay between 100 and 107 degrees. It is NOT greening after the rain.
In any event, I wouldn"t plow up what you have now. If you plan on replanting, I"d wait until fall, when you have some promise of rains and temps that would allow new grass to germinate and grow. Plow now and you"ll have nothing but dust for the next couple months. (IF you can even get a plow in the ground)