The water pump is
12v, so it’s not necessary to have the inverter on to use it. The most obvious thing of course is making sure the pump is switched on. I’m assuming you did that though, so the next thing I’d check is your DC distribution panel and see if the water pump fuse is burned out. If not that, then you’re probably looking at more involved issues, like the pressure switch being bad.
Another thought - is it not turning on at all, or it hums but you don’t get water? If the latter, it just needs to prime itself, which can be resolved by opening a faucet and letting it run for a bit.