Right, connect a fan either to a MOLEX directly off the PSU or to a MB fan header, but not both. Neither fan will power up when connected to a MOLEX or a MB header?



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Your MB has headers labeled - SYS_FAN1, SYS_FAN2, and SYS_FAN3.
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SYS_FAN2 will accept a 4 pin PWN fan, (automatic speed control based on temp settings), but it will also work with a 3 pin non-PWM fan as well, (the last pin will not be engaged when you plug a 3 pin connector into it).
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When using the MB SYS_FAN headers for fan power you have some control of the fans via the BIOS settings. In the BIOS under PC Health Status you'll find these settings,
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Plug the 3 fans into the three SYS_FAN headers, set Smart Fan Control to Enabled, and set CPU Smart Fan Mode to Voltage. There you should be able to fine-tune you fan speeds by setting different voltages for different fan speeds. It will take some experimentation to find a balance between cooling and quietness.
When the fans are connected to the MB you can also view your fan speeds when in the BIOS's PC Health Status. Keep in mind that your case fans have a maximum speed. If they don't move enough air you can easily replace it with a higher RPM fan.
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When using the MOLEX connector you can't monitor fan speed or control the fan through the BIOS settings. You can, however, control the speed with an add-on Fan Controller Panel. Or, if the fan's too loud running at 100%, you could replace it with a slower speed fan. Generally, a fan that runs 1000-1200 RPM max running at 100% will not be very noticeable for noise, while a fan with a maximum RPM of 1600 or more will be rather loud running at 100%.
If I were you I'd replace the MOLEX fans with some with 3 pin connectors. Get some with a maximum RPM of 1600 to 2200 or so. Then you could throttle them back to 1000 or so for quiet operation or crank them up of gaming via different BIOS profiles.
It takes me a lot of trial and error to get the fans and airflow as I like it. I have a small Lian Li that has five fans controlled through the BIOS with connections through the MB fan headers and a big Lian Li that has five fans all controlled by a single 3 speed switch - Low for quiet and high for gaming. The good part is that all of that stuff is relatively cheap so it doesn't cost a lot to try different setups.
The 3 speed switch is integrated into the case - Not available for purchase separately. Are all the fans 120mm and do you want LED or non-LED fans?
For the 140 I'd recommend Xigmatek or Cooler Master.
For the 120s - Cooler Master, or to move a little more air, Masscool or Xigmatek.
I'd also pick up a couple of Fan extension cables to make sure you can get the fans connected where you want.