Just wondering if the shore power where you were plugged in might be the problem? Its not unheard of that shore power plugs, especially in older and not-so-well-maintained RV parks can have problems, which is why you should ALWAYS use a surge protector. Are you sure the circuit breaker for the 30 AMP plug you tried was not tripped or turned off? I'd try your A?C again while plugged in to a 30 AMP outlet that you KNOW is working properly. If that doesn't work, you definitely need to go to a good repair shop.
Also, since you're new to to the world or RV'ing, you should know that your rig's inverter will run some of your smaller 120 volt accessories, like TV's, making you think they are working off the shore power, when they're actually running on the power from your coach batteries.
RV's have complicated systems; both 120 volt AC power that can come from either shore power or an on-board generator and 12 volt DC electrical systems that get their power from either or both your coach batteries and your chassis cranking battery, plumbing systems that use either on-board water or plugged in to 'city water'. And sewer systems that can either store waste water or run it in to a drain. You should have at least a basic understanding of these systems, how they work and how they are inter-related, before heading out on the road. Not saying you need to be able to repair them (altho that helps) but you do need to understand how they work and do what they do.
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