Yes, you can claim the AOC, assuming your parents didn't already claim it the maximum 4 times allowed (2015-18 is four tax/calendar years, so there's a good chance they did). You'll have to check with them. If so, you would still qualify for the Lifetime Learning Credit (LLC) but that's not as generous.
You are correct, you do not qualify as their dependent. At $40K salary, you most likely meet the earned income support test and it should not be necessary to run the support calculations.
If Turbotax (TT) is not giving you the AOC, you'v answered something wrong in the interview (other than the 4 times thing mentioned above)
If you declare $2156.50 (4000-1843.50) of your scholarship as taxable income, you can use the max $4000 of tuition to claim the maximum AOC. Declare the full scholarship as taxable to claim the maximum LLC.
