Q. They said the 1099-B was correct and complete, so I should call the IRS?
A. No. They can't help you. You're expected to know the answers to these questions from you own records.
Q. How can I enter this 1099-B in Turbotax Premier?
A. For sale category, select Box E -long term non covered (this is almost always the correct category in your situation).
You get the cost basis from your own records.
Unknown cost basis
You have to report the sale on your tax return. Lacking any cost basis, the IRS will consider the entire sale amount as taxable. So, you need to make your best effort to determine the original cost basis, even if (worst case) it's a guess. Historical prices of publicly traded stocks are readily available on the internet and should, at least, satisfy the IRS that your basis wasn't zero; just "google" “Historical Stock Prices". I use http://bigcharts.marketwatch.com/historical/. The stockholder relations dept. at the company may be able to help.
Unknown Basis
https://ttlc.intuit.com/community/investments/help/how-do-i-find-a-stock-s-cost-basis/00/25750
Unknown Basis & Date
https://ttlc.intuit.com/community/investments/help/how-do-i-find-a-stock-s-cost-basis-if-i-don-t-kno...
