I have 1099-B with no cost basis or date acquired info listed. The proceeds were only $2.01. How do I figure out what to put in these two boxes?

Enter a cost basis of Zero dollars and make up date as best as you can remember.  Then you will simply pay the income tax on the $2.01, which won't be much considering the headache you will go through otherwise. The IRS won'r ding you because you are not screwing them out of any  tax money.