I second the thought that reflux could be a culprit -- my dd had it, and the angle on the carseat just really aggravated it. She would cry until she puked if I couldn't calm her down (or at least get to the backseat or stop the car). And then she was unresponsive to me for hours, sometimes an entire day (no eye contact, no smiling, seemed exhausted). So letting her go wasn't an option for me.
A couple things that worked for me:
1) Strapping her in the carrier and swinging it around until she fell to sleep or got really calm, then attaching it to the base. I used to have to do this multiple times while driving as well. I'd pull over, take it off the base, and swing swing swing. This is what I did if I didn't have the option of #2 below.
2) Nursing her while she was in the seat. It was the only thing that worked for us for a good long while.
3) Singing. Sometimes I'd sing to her the entire trip. She didn't like CDs or music, she liked to hear my voice singing a familiar song. So, sometimes I'd sing her silly (or not silly) songs that I'd made up. I'd sing them to her when we weren't in the car, looking straight at her and smiling, and then those same songs could sometimes calm her down while driving.
Eventually she grew out of it, but traveling was difficult for a while! Best of luck.