well I own a manual Transmission, but knowing a thing or 2 about cars in general, let me pose a couple questions...
Are you leaking transmission fluid?
Pull the dipstick for the transmission fluid (not sure if AT integras have 1 or not for AT versions) does the fluid smell burned up?
When is the last time you have the AT filter and fluid changed? a clogged filter or even low fluid levels can cause this.
I suggest you have that transmission serviced ASAP and don't keep driving with it like that. the more you drive & do whatever it is you are doing to get it in gear etc... the more damage you are doing to it in general. AT are expensive to repair once you grenade them. get it fixed or start hunting for a spare ASAP cause it will be far cheaper to do a swap than a rebuild...