An information processing apparatus which is capable of, when hang-up occurs, eliminating the hang-up state and restoring to a normal state without bothering a user. A first power supply unit supplies power to predetermined devices among a plurality of devices, and a second power supply unit supplies power to the plurality of devices. When startup is done with power being supplied to the predetermined devices, software is started by supplying power to all of the plurality of devices. When the second power supply unit is turned on during the startup, whether or not the software has been normally started is determined. When the software has not been normally started, the software is restarted by carrying out an off-on process in which the plurality of devices are reset, the second power supply unit is turned off, and then the second power supply unit is turned on again.