I use to work for one of the major airports. One of my duties was preparing "permission to operate letters" for new airlines. It feels like I did prepare about a hundred of those between 1994 and 2001. I can only think of three passenger airlines (flying transport equipment) that are still around today that were started (read totally conceived) between 1978 and 2001.

I don't include any of the regionals or commuters because they are proxy airlines not real airlines.

America West (now purchased USAirways and retained that name)
Midwest Airlines
Airtran (formerly ValuJet)
Jetblue

Onfinal