Since you were gifted the fund, your basis is the donor's basis for a starting point. All you can do is get as close as possible using what data you can for the year of the gift. Once established, make adjustments for stock splits, dividends, and capital distributions. See About Publication 550, Investment Income and Expenses page 39 for gifted details.
You should be able to do historical research to determine dividends paid so you can move backwards to your beginning basis. I am sure these were all DRIP (reinvested dividends) since you were young. Once you determine a reasonable share basis for the starting point along with a reasonable price paid for those shares initially, you have your starting point. You have great data to use to make adjustments and get your correct final basis.
All you can do is your best. Remember, if the IRS decides to audit this area, they will also have to find historical records. So, if you have good, solid, reasonable, research showing your methods, that should be sufficient.
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