Did any major events happen once the Kali yuga started? Like an earth quake or major disaster? Or was it more of the same day?
The Kali Yuga began when Krishna departed the Earth. Here is how this chapter of the Mausala Parva of the Mahabharata describes the omens that were seen at that time:
When the thirty-sixth year (after the battle) was reached, the delighter of the Kurus, Yudhishthira, beheld many unusual portents. Winds, dry and strong, and showering gravels, blew from every side. Birds began to wheel, making circles from right to left. The great rivers ran in opposite directions. The horizon on every side seemed to be always covered with fog. Meteors, showering (blazing) coals, fell on the Earth from the sky. The Sun’s disc, O king, seemed to be always covered with dust. At its rise, the great luminary of day was shorn of splendour and seemed to be crossed by headless trunks (of human beings). Fierce circles of light were seen every day around both the Sun and the Moon. These circles showed three hues. Their edges seemed to be black and rough and ashy-red in colour. These and many other omens, foreshadowing fear and danger, were seen, O king, and filled the hearts of men with anxiety.
And here is how Yudhishthira describes the omens in this chapter of the Srimad Bhagavatam
Just see, O man with a tiger’s strength, how many miseries due to celestial influences, earthly reactions and bodily pains — all very dangerous in themselves — are foreboding danger in the near future by deluding our intelligence. The left side of my body — my thighs, arms and eyes — are all quivering again and again. I am having heart palpitations due to fear. All this indicates undesirable happenings. Just see, O Bhīma, how the she-jackal cries at the rising sun and vomits fire, and how the dog barks at me fearlessly. O Bhīmasena, tiger amongst men, now useful animals like cows are passing me on my left side, and lower animals like the asses are circumambulating me. My horses appear to weep upon seeing me. Just see! This pigeon is like a messenger of death. The shrieks of the owls and their rival crows make my heart tremble. It appears that they want to make a void of the whole universe. Just see how the smoke encircles the sky. It appears that the earth and mountains are throbbing. Just hear the cloudless thunder and see the bolts from the blue. The wind blows violently, blasting dust everywhere and creating darkness. Clouds are raining everywhere with bloody disasters. The rays of the sun are declining, and the stars appear to be fighting amongst themselves. Confused living entities appear to be ablaze and weeping. Rivers, tributaries, ponds, reservoirs and the mind are all perturbed. Butter no longer ignites fire. What is this extraordinary time? What is going to happen? The calves do not suck the teats of the cows, nor do the cows give milk. They are standing, crying, tears in their eyes, and the bulls take no pleasure in the pasturing grounds. The Deities seem to be crying in the temple, lamenting and perspiring. They seem about to leave. All the cities, villages, towns, gardens, mines and hermitages are now devoid of beauty and bereft of all happiness. I do not know what sort of calamities are now awaiting us. I think that all these earthly disturbances indicate some greater loss to the good fortune of the world. The world was fortunate to have been marked with the footprints of the lotus feet of the Lord. These signs indicate that this will no longer be.