I think the Wal-Mart batteries have a pro-rated warranty for a period of time after the free replacement period so I would suggest letting them test it. If they say it is good you could take it to advance or autozone and let them test it and your alternator.
I went thru a similar issue with my Mother's Lexus LS400. Turned out to be the starter. Took me about a month to figure it out.
I went thru a similar issue with my Mother's Lexus LS400. Turned out to be the starter. Took me about a month to figure it out.