Air India — regarding incorrect flight information

I was informed that my flight from hyderabad to coimbatore on 31mar was delayed by 2 hrs from the actual departure time 9:35. When i booked the ticket on 27 mar, the flight departure time was 9:35 but when i took boarding pass on 30 mar, departure time was mentioned as 11:35. So i reached airport at 10 am on 31 mar. But when i completed my security check,
Duty manager ms. Atheeka sultana called me and said that the flight had already started. Upon discussion i came to know that it is because of the system fault i got wrong information. Initially they said that they can give alternate flight in jet airways. Then later they said they don't have any direct flight and they can't give seats kn connecting flight. They are not ready to pay the extra fare which i have to pay for the other airlines as i have to travel on the same day. It is because of their mistake i have to spend 3500 bucks again from my pocket. When i asked about the same, ms. Atheeka sultana told that i can claim that amount with the air india by submitting new ticket, but when i asked for a written confirmation she was not ready to give that too. The way she behaved with me was totally upserd. I need proper justification for the issue which was made by air india.