can it really not shift from a dead battery?

i have a 1992 camaro rs with a 305 and 700r4 auto tranny. i just traded my 1988 honda crx with a b18swap for it and i must say im not too happy with it soo far. it has a edelbrock manifold and 4 barrel carb. cammed up with forged pistons and 3 inch dual exhaust. i dont know how big they are stock but its alot bigger than the stock exhausts im used to seeing.

the person who sold it to me said there were no problems with the tranny slipping or nothing. the first nite i had the car it died on me and woldnt jump back up for a while which i later leaned the choke was stuck on a lil bit. from the beggining the car woldnt shift into 3rd unless i would have it in overdrive and redline the car and feather the gas. it was like it was in neutral instead of third. then it wouldnt shift to 4th and kept going back into second redlined again.

i was looking into it and learned that a number of different electrical problems or blown bulbs and fuses can stop a tranny from shifting. my battery wont charge and runs without being hooked up at all. i have tranny fluid and its a good red color still and has propper amount. i dont know what else it could be so im hoping people can help me out. i need to be able to make it to the hospital when my kid is born this month and cant drive on the highway in 2nd gear with a v8. my only other thought would be i got the screwing put to me

Although whatever the charging problem is.........

It is highly unlikely to do with the trans. How is the trans from dead stop into second?

Possibly a bad vehicle speed sensor, doesn't always throw a code either.

My other thought is the the throttle valve cable is out of adjustment, but usually the trans will have a hard time getting up and going, then all gears after that will feel "slippy".

Otherwise, I would be more inclined to think you have a sevro or band failure or possibly a bad valve body or missing check ball.

its fine from first and second but when its supposed to shift into third it starts slipping or goes in neutral. then when i hamer it up to redline and feather the gas it shifts into 3rd but i can get overdrive to kick in. not sure if it has a shift kit or not someone said it might when i bought it off them but i noticed while looking under it there is no cover or bellhousing on it and the torque converter and flywheel are exposed and the atf oil pan is smashed in. every now and then i her something clunking around some sort or chunk of metal and i believe its coming from the tranny. i just got it last week and have had only problems with it

the atf oil pan is smashed in.

That could very well be a huge part of the problem ther. Crushed the filter?