Toyota Yaris help!

Ok so im deployed and my wife is having issues with our car and I cant get eyes on so forgive me for the 3rd person perspective. My wife went to go start our car (2008 Toyota Yaris) and the car would not start. She jumped the car and once the car started she immediately removed the cables and the car died instantly. She went back and jumped the car again but left it running with the cables on for about 30 minutes then the car stayed on once she removed the cables. She got in the car and when she went to shift it would not shift out of park, said it was almost like the car was off, shifter wouldnt budge. She also said that whenever she tried to rev the engine it would not rev and there were no strange noises that she heard. She also said that when she tried to rev the engine the car made noises like the engine was going to die. We have asked a few friends and they all said it was probably the alternator. i ordered one and will have a buddy install it but i just wanted to get another opinion so i know what to expect. Thank you for your time!