If you have an Intel CPU based on socket 775 you can use the eraser to clean its contacts, and then use the toothbrush wet in isopropyl. If your CPU use pins (e.g. AMD CPUs, old Intel CPUs), then you can’t use the eraser as you would break the pins. In this case go ahead and use the toothbrush wet in isopropyl.

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Figure 9: Clean the CPU contacts with an eraser (only for socket 775 CPUs).

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Figure 10: Then clean them with a toothbrush wet in isopropyl.

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Figure 11: Cleaning an AMD CPU with a toothbrush wet in isopropyl.
After cleaning the parts you need to clean their sockets on the motherboard. This should be done with the toothbrush wet in isopropyl. Never use the eraser on the motherboard.

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Figure 12: Clean the CPU socket with a toothbrush wet in isopropyl.

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Figure 13: Clean the memory sockets with a toothbrush wet in isopropyl.

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Figure 14: Clean the video card slot with a toothbrush wet in isopropyl.
After cleaning everything as instructed and giving enough time for the parts to get dry, install the CPU, the CPU cooler, the memory module and the video card back to the motherboard and try turning the PC on.
If it turns on, great, you solved your problem. If it doesn’t, then proceed to the next step.