Transmission issues on 1991 Acura Integra

when i start my car nd i get going down the road i get through first gear second gear and third and when it goes to go into forth it slips out like the cars in nuetral i have a 1991 acura integra rs and its an automatic Plz help tell me whats wrong with my car also when i give it gas the battery light comes on and all my lights dim and my car starts to dye out

Asked by for the 1991 Acura Integra
2 things,

1) It sounds like your clutch is slipping, that is why it feels like neutral in the higher gears.

2) It also sounds like your charging system is not working correctly, possibly you may have a really weak battery. Do yo ever have to jump start your car? I have seen Acuras do this, they will almost die when yo give them gas and the battery light will come on because there is no reserve let in the battery and the Alternator can not supply enough power under acceleration at night, because lights are on etc.