If you're "really interested"...
23rd century bc - akkadian becomes lingua franca of mesopotamia, along with lesser-spoken sumerian in hold-out city states. Related semitic dialects are spoken in Canaan.
18th century bc - Semitic-speaking Ammorites invade Akkadian land, Akkadian is retained as the "official" or "court" language (re. Hammurabi), but the general populace now in northern Canaan, northern Mesopotamia, and a bit east generally speak the Semitic dialect we now know as Aramaic.
15th century bc - Earliest known records of proto-Iranian, an indo-European dialect/derivative. Spoken by the Elamites from south-western Iran. These people consistently warred with Mesopotamian rulers for centuries and lost. The court language becomes Akkadian, as we see in their inscriptions. Indo-European dialects were spoken for hundreds of years in western Iran, but these are the first written examples of what would "become" Farsi.
14th - 10th century bc - With little to no powerful Mesopotamian empire to speak of and exert cultural influence, western Iran resumes(or for the most part continues) to speak proto-Iranian
9th-8th centuries bc - Conquests by Assyria. Sargon II (in 715)evicts and exiles Mede kings, and while Medes had been paying tribute to Assyria for some time, cultural influence spreads, including semitic languages Aramaic and retained court language Akkadian, (kinda like how we still use latin for many legal and scientific terms today in english). I guess it's a little like Aramaic was to the territories bordering ancient mesopotamia what English is today. Altho every country has it's own language/dialect, to be involved on the world stage mostly involves English.
6th century bc - Achaemenids come to power, adopt a dialect we refer to as Imperial Aramaic to maintain communication and congruency across their vastly growing empire. During this time the dialect we now know as "old persian" was spoken widely in western Iran, as the Achaemenids were indo-iranian peoples, now beginning again to spread their culture.
So, did Darius speak Old Persian or Imperial Aramaic? The answer is likely both. When talking to friends and family he spoke Old Persian. When passing edicts, though, and otherwise communicating with distant parts of his empire, he spoke or wrote Imperial Aramaic.
But from the start most of you probably didn't realize why Persians take such offense at Darius speaking Aramaic. It's because Aramaic, like Arabic, Akkadian, Phoenecian and Hebrew, is a semitic dialect.