If parent gives you 2770 shares on TOD at a price on 13.9, do I get the new stock price at TOD or when given to me?

"TOD" = transfer on death, correct?

Since you inherited these shares, your cost basis is the fair market value of the shares as of the date of death of the decedent. In some rare cases an alternate valuation date is used which is 6 months after date of death, but this is rare and only comes into play if the executor had to file an estate tax return and chose to use the alternate date - if you're not sure about it ask the executor.