Both inverters died and now the one's fan runs constantly

Hard to say whats going wrong. Pickup a multimeter at Walmart and check your voltages. At the solar controller, at the battery, at the inverter, even coming out of the inverter if you want.

I have a 400w no-brand inverter I use to charge my laptop sometimes, and its fan runs too. The laptop has a 110w charger, so that's more than 25 percent of the inverter power, I guess the fan runs when it needs to.

Charging a phone is only going to need 5-6 watts, so that's a big difference from a laptop.