While I'm on LG, I heard a loud start up sound and it is the HVAC blower fan running, but heres the weird part. The thermostat is not even on cool or heat mode! The thermostat is off, even though the blower fan, keeps on blowing. Plus the fan control on the thermostat is on auto. But even though, its not on the cool or heat mode settings, its off. Could this be a circuit issue or something? Because the fan is on auto, but cool and heat modes are off. It just likes to kick on the blower fan randomly, even though, I don't hear a click from the thermostat.

Could be a faulty control system.

Mine has a "diagnostic mode" where there is a lone red LED on the circuit board. You have to unscrew the blower panel to see it. There is a code where the lamp has a "normal" flash and "coded" flashes that indicate a malfunction. Furthermore, when the circuit board is in the fault indicator mode, the blower never stops. There are two reasons for that. First is safety where the malfunction could be a slightly overheating part, in where a continuously operating fan is beneficial. Second, it serves to alert the occupants that there is something wrong. In the event of a seriously overheating heating component, I hope there would be an immediate complete shutdown to avoid fire.

Before calling for service, try to shut off every circuit breaker that feeds the system (normally there is one for the air handler and one for the outside unit). Wait 30-60 seconds and turn them on again. Sometimes, the control circuitry can get confused, especially if there were instabilities in the mains or if there was lightning recently. (Although rare, lightning can happen in winter during a snow storm, it is commonly called snow thunder or something along those lines.)

Also, does your system have more than one zone, where another thermostat in the system turns on the fan ? That could explain the absence of clicking at this thermostat (the one closest to you when it happens).

@sol, blower keeps going, but then it turns off, after 22 minutes.

My system is a Goodman HVAC system, theres two of them, one for upstairs, and one for downstairs. The downstairs one, keeps turning on the blower, and shut off for 22 minutes, not the upstairs.  Plus, I don't know how many zones it has. But I do know the condenser outside, is not a heat pump, its a straight cool unit, plus its a Goodman condenser. I don't know how many BTUs it has.

Well the best I can offer is to cycle all circuit breakers that feed it and see what it does. If it doesn't rectify the issue, it seems like it would be time to call for service.

I put it on cool mode, and it works. So it could be that the PIC (Programmable Intergrated Chip) on the circuit board, must be confused. Because now it works.

While I'm on LG, I heard a loud start up sound and it is the HVAC blower fan running, but heres the weird part.

I also think that there is a problem with the motor of the fan of your HVAC system, as all of our A/Cs (Central or ductless), don't have any start-up noise for their fans when they turned on.

Also: some A/C can be operated on a ventilation mode, where they only circulates forced air without heat or cool it, similar to a regular fan. But you say that the fan operated without you do anything, so most probability the controller of your HVAC is defect.

It could mean a wiring problem. A short circuit may bypass the fan relay contacts and so make it running. There are few aspect what would point to that:
The BANG at the startup: Normally some kind of "dimmer" like circuit (or gradually go over the fan power settings) is used to soft start the fan (to prevent that noise), but if the power is applied via shorted wires in a cable, there is obviously no soft starting, hence the abrupt start with its noise.
Confused control would start the fan using the soft start as well, so without that unusual noise on the blower motor start.
Plus if the short circuit just happen to apply power to the fan and nothing else, the unit may still be able to perform normally: The cooling is controlled by the valves (see below), so nothing prevent its ability to maintain the set temperature.

The "thermostat clicking":
With many system designs the internal units have electromagnetic valves in the cooling loop (to isolate it from the condenser unit, when not cooling, to prevent condensation and parasitic heat transfer when other inner unit is supposed to cool so the condenser is running), so the "thermostat clicking" is actually not the thermostat, but these valves (as they are operated directly from the thermostat function, you may get confused about the noise source).
Usually once the thermostat turns ON, it starts the fan, as well as opens the valves. Once the thermostat shuts OFF, it shuts off the valves, but still keeps the fan running for some time (to utilize the accumulated coldness and mainly prevent extra humidity accumulation and consequent water dripping). This delay was done via a thermal relay, in modern units it is of course an electronic timer or even a firmware feature in the microcontroller.
The thermostats alone use to be very quiet (even the simple bimetallic mechanical ones, some older even used the mercury tilt switch), some modern ones may be using solid state controls, so completely quiet. Of course, this can not silence the valves, so the system is still clicking when activating/deactivating. The fact this clicking is missing means the power goes just to the fan and not to the valves.

Well I have a Honeywell electronic thermostat that has a LCD screen with buttons, plus my HVAC systems are modern, so it could be a PIC in the circuit board could be confused.

  it could be a PIC in the circuit board could be confused.

If the power flickers a bit or does a real quick on/off, that can/does easily 'confuse' (or put in some weird mode) IC chips.
Simply turning off the breaker for a minute & then back on will re-set it (just like rebooting a computer)

I'll try that, when I have the time, ok.