Hello,
Most boards will have some kind of FAN RPM profile enabled, depending on this preset it may be to low for it to start when the PC has been off for a while.
To check enter the BIOS and disable the FAN profile, PC Health section.
CPU Fan Speed Control: set to full speed
1st system fan speed control: set to full speed.
...
See what happens when you turn on, should be max rpm, if not you got something else going on
The VGA is not part of the motherboard controller and will have its own fan profile determine by its own BIOS.
Same kind of thing too and you should have noticed this before or is this the first time using the GFX card?