The True Power itself didn't cause Ishamael to go mad entirely - it was mostly being released from the Sealed Bore at forty year intervals that caused him to go mad, in my opinion. He wasn't affected like Aginor and Balthamel who were close to the Seal, being ground down until they were old and practically walking zombies due to Ishamael being released every forty years and allowed to walk in the world instead of being in suspended animation.
It can be assumed Ishamael was released from the Sealed Bore a short time after Lews Therin and his Hundred Companions sealed the Bore with their attack on Shayol Ghul - from there he more or less directed what was left of the Shadow's rapidly scattering armies, and after forty years, wound up back in the Bore, which led to Latra Posae Decume (the female Aes Sedai who initially opposed Lews Therin's plan to Seal the Bore, and opted for the building of the Choedan Kal, in order to erect a shield around Shayol Ghul, so the Aes Sedai could discuss and figure out what to do next - the foolish woman) uniting fragments of the Light's military and etc., earning for herself the name Shadar Nor.
Ishamael most likely began operating as Ba'alzamon sometime before the Trolloc Wars; thus, by the time The Eye of the World begins, between using the True Power, and being released from the Sealed Bore every forty years, mostly everyone seems to think Ishamael is the Dark One (because if it's repeated often and its mysterious/unknown to the populace, aka if enough people believe it, that belief will spread), including Ishamael himself.
Ba'alzamon becomes synonymous with the Dark One, despite it only meaning "Heart of the Dark" in the Trolloc tongue.
And no sane person could bluster and blather the way he did - that is, unless, one looks at Lews Therin.