You can buy a car without a SSN so long as you are not financing it. Well even that depdends on where you do it.
I don't want to add to your stress, Sara, but if Dave needs to drive, I would suggest looking into the driving license rules in Minnesota.
What we found in Illinois was:
You need a SSN# to get your driver's license. You might be able to buy a car, but in order to get it insured, you need the Illinois license. Also in Illinois, you can drive on a foreign license for 90 days, before getting the state license. It's kind of a catch 22: You can get a car, but you need a valid state license to get insurance. To get a license, you need the SSN#...
You can rent a car on an English license, but that gets expensive.
The Illinois Rules of the Road are available on line. I'd suggest looking into Minnesota's because I don't know how urgently Dave will need a car.
I know there are tons of details and I don't want to do your head in; I'd just feel bad not relaying information that we found out, having just been through the ropes....