What was the average air fare in US dollars from Mumbai to Minneapolis (return) in Aug 2004? Is there any database available anywhere?
First of all your question is much more complicated than it sounds. Air prices are not exactly "fixed" in advance but they are constructed from building blocks automatically depending on many circumstances and factors. (See How do airlines determine ticket prices?)
The International Air Transport Association may have the tariffs each carrier was levying in its printed interline tariff manual for that year. Unfortunately the cost of purchasing the manual was about 800 US dollars and I doubt it is still in print. I could not find any reference on the website.
In terms of a database, the historical fare display I have only goes back twelve months, which is only as far as is necessary for historical pricing information (airline tickets expire after one year).
Even then this will not tell you the "average" price (which is quite a complicated question because of the extensive price discrimination airlines apply), but only what different prices were available to public consumers depending on many conditions.