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You may report a $0 cost basis or you may construct a cost basis.  The issuer of the IRS form 1099-B does not have the original cost or the issuer would have reported it.  The IRS does not have it.

There are several issues:

• The basis of the original gift is likely the basis of the previous owner (with the exception listed below from the TurboTax Help.
• The basis of the additional shares purchased by the grandparents is the amount of the dividends reinvested.
• The basis of additional shares purchased after the gift by the grandparents is the amount of dividends reinvested.
• A stock split does not change the cost basis.  For instance, you own two shares at $10/share = $20 cost basis.  If the stock splits into four shares the cost for the four shares remains $20.

It is possible to construct a cost basis if you have a spreadsheet and are so inclined.  You would research the historical cost yourself by using a tool returned under a Google search for 'historical stock price lookup tool'.  

Or PSEG shareholder services may be able to provide:

• a historical cost lookup, 
• a record of dividends reinvested per share, and/or 
• a history of stock splits.

This TurboTax Help states:

Gifts

The basis of securities you receive as a gift depends on whether your ultimate sale of the stock produces a profit or loss. If you sell for a profit, your basis is the same as the basis of the previous owner.

In other words, the basis is transferred along with the property. If you sell for a loss, though, the basis is either the previous owner's basis or the value of the stock at the time of the gift, whichever is lower. In other words, you don't get to write off a loss that occurred while the donor owned the securities.

The sale is reported on IRS form 1099-B.  To enter the form manually In TurboTax Online, follow these steps:

1. Down the left side of the screen, click Federal.
2. Down the left side of the screen, click Wages & Income.
3. Click the down arrow to the right of Investments and Savings.
4. Click to the right of Stocks, Cryptocurrency, Mutual Funds, Bonds, Other (1099-B).
5. Click Add investments.
6. On the Let's import your tax info screen, select Enter a different way.
7. On the OK, let's start with one investment type screen, select Stocks, Bonds, Mutual Funds, then Continue.
8. At the screen Which bank or brokerage, enter the information.  Click Continue.
9. Do these sales include any employee stock, enter No.
10. Do you have more than three sales, enter No.
11. Do these sales include any other types of investments, enter No.
12. Did you buy every investment listed, enter No.  Continue.
13. On the screen Now, choose how to enter your sales, select One by One.  Select Continue.
14. At the screen Look for your sales on your 1099-B, select Continue.
15. At the screen Now, enter the sale, enter the information.  Under Sales Section, you would select Long-term Basis not reported to the IRS.
16. Select The cost basis is incorrect or missing on my 1099-B.
17. At the screen We noticed there's an issue with your cost basis, select I know my cost basis and need to make and adjustment and enter the Actual cost basis.

Retain any cost information that you collect with your tax return papers should a tax authority have a question about the cost basis at a later time.