What model is your Vista panel? The Control Panel, not the keypad. "Vista" is the name for a series of control panels, kind of like a "Maytag" fridge. All Vista panels have much in common but there are differences. One difference is that some don't have fuses and some do, and those that do, have them in different places. Pulling a fuse out and then returning it usually doesn't blow the fuse.
The first thing I'd check is whether your panel's transformer is plugged into its outlet, and working; and whether that outlet has 120V power. Statistically, the most common causes for batteries going low is a popped circuit breaker to the outlet, or transformer got unplugged and left out. Less common is that transformer burned out (fairly rare) and isn't supplying the necessary AC power to keep the battery charged.
If the transformer is not supplying AC to the panel, then disconnecting the panel battery to change it will power the panel down. Once it's powered down, a new battery will not power it up again unless the panel is receiving AC power. This prevents a lot of users from draining a new battery if they don't notice the AC power to their panel is out.
