My father passed away in August of 2007. He had very little money, however he did have a CASH account in a mutual fund that was worth a little over $70,000 when I dissolved the account.
Since it earned dividends each year, wouldn't he have reported those as income each year on his tax return? So am I only responsible for the 2007 dividends earned or the difference between the basis and what it sold for?
Thanks!

The executor of the estate is responsible for filing an income tax form on behalf of your Dad's estate. His income would include dividends earned in 2007 - you (or the executor) should have received a 1099-DIV that details the amount earned. Any taxes owed come out of his estate - this should be paid befire his assets are distributed to his heirs.

You do not need to wory about income he may have received in prevoius years, as he should have reported those dividends previously. I assume here that there are no capital gains issues (being a cash account, not a mutual fund with stocks or bonds).