Box-2 and Box-3 of 1099-Q are empty

You can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. You cannot double dip! When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records.
Otherwise, you have to manually calculate the earnings portion of the distribution, from your own records (you could first ask the plan administrator for help). It may best be explained by example. Your box 1 (distribution) was $2000. The fair market value is $8,000. That means at the beginning of the year you had $10,000 (8000 + 2000 = 10000) in the account. Over the years, you contributed $6000. That means that $4000 (10,000 - 6000 = 4000) of your account was earnings. That means that 40% (4000 / 10,000 = 40%) of any distribution was earnings.  Basis is box 1 minus the earnings.

"I have no way to determine the cost basis as it was contribution over a long time".  Lacking any cost basis, the IRS will considered the entire box 1 amount as taxable. So, you need to make your best effort to determent the original cost basis, even if (worst case) it's a guess.