Hi ghuston,
Welcome to the Heartland Owners Forum.
First off, an inverter changes 12V DC into 120V DC. The only inverter that Heartland ships would be the one that runs the residential refrigerator when not plugged into shore power.
If you mean the converter, which changes 120V AC into 12V DC to charge the batteries and provide power to interior lights and other things, it's possible that while changing the batteries, you might have inadvertently done something to blow the on-board fuses on the converter. There are 3 blade-type fuses.
It's also possible you tripped the 12V DC manual reset circuit breaker on the buss bar near the batteries. There's a teeny-tiny reset button on one end of the breaker. See attached picture. The breakers are covered by a red rubber boot and yours may look different from the picture. If the interior lights work on shore power, but go out immediately when shore power is disconnected, and your battery has a charge and the cutoff switch is ON, the breaker has tripped.
You can check converter output by cycling the auto-level panel to show DC voltage. If on shore power, it will typically show 13.2V DC or higher. If 12.6V DC or lower, the converter output is not getting to the batteries.