What could it be that will make my BMW 1997 528 I 5series stop running out of nowhere when I just drove it about 15 minutes before that? (Hasnt started since then.)

What is your question?

My fiance just got the BMW 528i 1997 5 series for her birthday from a friend. One day we drove a fine no problems and we came home parked it turned it off in a little later that night I came out and the car started sounding an alarm when I try to turn it on. I checked it out of oil at spot a brand new battery replaced all the bulbs that lights are out and nothing seems to work it does not say that it is in security mode or anything like that. All the lights come on the still Sound the Alarm sometimes when I try to start it but not all the time it just cranks and doesn't start. When I have the key like if I'm going to turn the car on and it's an about first position I hear it buzzing noise by the battery sometimes in the trunk and sometimes I hear a buzzing noise by the fuel pump in the front under the hood. The only problem with this car that I've seen so far other than and not working out is that the radio plays when it wants not all the time it turns on in air conditioning doesn't always turn on . So if anyone can tell me what they think it could be are they have this pound before and they know what it is please let me know what the problem was with their car and how much was it to fix it. I would hate to have to get rid of such a nice car it was a gift to my fiance and help us out with work.