07 aveo 5 randomly dies, new battery

I'm not a mechanical person by any means, so bear with me... I have a 2007 aveo 5, I bought used. Drove fine for awhile, then I noticed my dash lights flickering kinda crazy. That soon escalated to every time I hit my brakes my lights would dim and my radio would turn off. I changed the battery, that was heavily corroded and thought that would fix my problem. But sometimes when I try to start my car it shuts off completely. No power at all. I've found that if I shake the battery it will start. I can take off and drive for awhile, but then it will randomly die while I'm driving. I can get out shake the battery again and take off again for awhile. I'm thinking it has to be a lose cable or a bad connection somewhere. Maybe I need to change my battery cables? I know very little about cars and would appreciate any help. Thanks!!