92 prelude wont start help!!!?

my prelude chooses when and where it wants to start its completely at random. this is whats going on. when i open my door the hazards start blinking and theres a little chime as if i left my lights on. i try to start my car and everything turns on but theres no cranking, ive been told it may be the battery cause sometime when it wouldnt start i would jump it and it starts but that also only works sometimes. i tried to start it this morning and it cranked over a couple of times and then the battery died. so i umed it was a weak battery that couldnt hold a charge very well. so i got a new one hooked it up properly all my connections are nice and tight. i tried to start it again and no cranking, i think it may be the starter but everyone told me its the battery. so any insight on what might be happening would be greatly helpful.