I'de start with the battery.
Eliminate simple things first.
A weak battery can cause all kinds of gremlins.
Go to an auto-parts store and have them test the battery.
Even if the battery is new, or not that old, it's still the best place to start.
If it is the battery, and the problem returns, then you obviously have something draining the battery.
That could be many things, so don't jump that far ahead yet.