Plugged in but ac won't work without generater running

Get a multimeter from Ace or similar hardware store and test the connections at the pedestal. All the items you listed could be DC powered and you don't really have AC available.

It would help if you filled in your profile so we know what you have.

Have you checked your breakers?

Moved from Forum Technical Support

Sounds like issue might be with your 'transfer switch'

The transfer switch swaps AC power from shore or generator to feed main AC panel

No AC from shore...OK from Gen---transfer switch stuck on generator input
Bad relays/burnt contacts etc.

what about other 110v items, TV, MW, coffee maker ?
do they work
your lights are most likely 12v, they and the water pump and vent fans will run on battery, until the battery is too low
when that happens your fridge might shut off, if it uses 12dc power for control

it sounds like the "transfer switch", this is a relay that auto switches between generator and shore power, the contacts are stuck

let us know what rv you have
somebody can tell you where to look for the BOX that is the ATS "automatic transfer switch"

when you find it smack it good with the flat of your hand, that might unstick it

I wonder if you have a very poor connection someplace that is causing such a voltage drop that the AC cant get enough current to start.

I had the exact same thing twice. Once it was the cord wasn't firmly plugged in and not making good contact. At that time I had an rv that I had to plug into the pedestal and the rv, the rv side wasn't making good contact. I disconnected both side and firmly reset them everything worked. Second time the pedestal breaker was bad. Good luck

if you are truly getting power from the pedastle then it is likely the transfer switch, had one go bad on me once and the mnfg told me it defalts to gen side. they sent me a new board and all is well.

We really need to know he RV and setup you're asking about!

For example, neighbor had a 33-ft Class A, two A/C units, 5500-watt generator, and 30-amp shore tie service. By design, it would run only one A/C on shore tie, but both on generator...

I agree, it sounds like your seeing things run off of the battery's and the shore power is not getting to your coach. Plug something into where you have your shore power plugged and see if you have power to that point and if so go to the other end of your cord going into the coach and check there. If you do its probably the automatic transfer switch" like the wizard said.