Processor Fan Noise: Any suggestions for reducing noise?

There are multiple things that could be going wrong here. Just because your fan is making noise doesn't mean your PC is overheating. BSOD wouldn't be able to occur if your CPU was fried because your CPU tells your PC to display the BSOD.

To solve this there a multiple things that you can check. First, I would check your power supply and ensure its not brining in too much current or power. If your power supply applies too much power (15V when your CPU can only handle 12V) will cause your fan to run faster.

Secondly, the thermal paste keeps the CPU attached to the motherboard and doesn't do much to cool the CPU so its most likely not the thermal paste. Lastly you could try re-installing Windows as BSOD mainly comes up with a software error and based on what you have said windows is the only thing installed. About the LAN port, you need a driver for any form of hardware to work, this may also be causing you to have the BSOD as it may be searching for a driver and can't find one thus leading to the error.

Hope this helps.

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