Sounds like you have 2 single pole breakers feeding the indoor unit where it should normally have a 2 pole breaker. Could be a short preventing the one breaker from resetting, or it could be the breaker itself is bad. In either case, you really need to change this out to a 2 pole as using a pair of single poles can create a dangerous situation. 2 pole breakers have what's called an internal common trip, which means if either hot leg has a short or overcurrent situation then both sides of the breaker trip so all power is disconnected.
That said, the indoor section would typically have a 220 x 24 volt transformer to supply control power for the system. One of your single pole breakers being tripped disables the transformer, thus nothing works at that point.
I'd first disconnect the power from the indoor unit and see if the breaker will reset. If not, the breaker is bad or there's a short between the breaker and the unit. If it does reset, then check each leg of the unit power for continuity to ground. That will show you which leg is shorted. From that point, use the unit's wiring diagram to chase down the location of the short.
My first guess is a bad breaker. If the fan motor locks up it usually won't trip a breaker because the impedance (resistance} of the motor is sufficient to prevent it from pulling enough amperage to trip. It just sits there and gets hot. Of course if there's an actual short in the windings then it would trip, but that's fairly rare from what I've seen over the years. The control transformer normally has an internal fuse, so if it shorts it just blows that fuse rather than tripping a breaker. Past that, most shorts are going to be due to something loose or something where the insulation is rubbed thru.
Regardless of what you find, get rid of those single pole breakers and replace them with a proper 2 pole unit. Real cheap way to get rid of a potential dangerous situation down the road.
