Mitsubishi Galant 2001electric problem

My mitsubishi Galant 2001 wouldnt start after turned off until I get jump. Advance auto parts diagnosed 58 acc on the battery and alternator needed to be changed. I'd changed the alternator but after couple hours drive srs indicator went on rpm went "0" temperature droped below normal and light dimmed a little bit and the car shut off completely and never started. I thought it was starter but when I got jumped it started fine but not for a long. I was driving with no head beams on and while I was driving the car would have hard shakes in between driving, it felt like it was turning off. What could be the problem. I was thinking the battery worn out due to alternator failure but im not completely sure. The rpm indicator would shut off while driving and come back again on and off. Thanks in advance.