Dalton was born in Newburyport, Massachusetts. He attended Dummer Academy in Byfield, Massachusetts, and graduated from Harvard College in 1755. Afterwards, he studied law and was admitted to the bar, but did not practice. Instead, he engaged in mercantile pursuits. He later served as a delegate from Massachusetts to the convention of committees of New England Provinces which met in Providence, Rhode Island on December 25, 1776. Dalton served as a member of the Massachusetts state house of representatives from 1782-1785, and served as speaker in 1784.
He was elected to the Continental Congress in 1783 and 1784, but did not attend. He served as a Massachusetts state senator from 1785-1788, and was appointed to the U.S. Senate in 1788. He served from March 4, 1789, to March 3, 1791. He was an unsuccessful candidate for reelection in 1790. Much later, he served as surveyor of the port of Boston from November 1814 until his death on May 30, 1817. He is interred in the churchyard of St. Paul’s Episcopal Church in Newburyport.