Make sure to still test the alternator. A new battery will last a little while, but if it is the alternator, you will drain the new battery as well.
Run the same diagnostic test from the OBC functions. It should stay up near the 140 or 14.0 reading (volts) when running. If not, your alternator is not producing, get it checked or you will get stranded again.
Countless threads here and other forums will point you in the same direction.