Here is my 2 cent diagnosis. You mentioned a grinding noise in the steering at low speed. If this is primarily when the car is cold it is potentially an indication that you have a loose belt or a belt slipping - could be a tensioner or need of a new belt. This in turn could also cause a dead battery as your alternator may not be fully juicing the battery.
I would check the belts for cracking and being loose, charge the battery and take it from there.
Good Luck