I would first open the case and check the 3 fans to see their condition. If you haven't ever done this, the inside is probably covered in dust. If you don't know how, go to Dells website and download the manual on the 8400. It is very clear and easy to follow.
Make sure the fan blades are clean. There is a fan in the front, back, and above the processor. I use compressed air at a low PSI, with an air dryer on it, to keep my machines clean inside. After I blow it out, I gently clean each fan blade with a soft toothbrush. The cleaner the blade the more efficient it is.
Restart the computer, with the case open, to see if the noise is gone. At the time you turn on the computer, listen to the hard drive also. If it is the hard drive you will hear it. Also, have another person put their ear to the area near the power plug in the back. If the power supply is making the noise the other person will hear it.
If the noise is coming from the hard drive. and if you know the brand of hard drive, go to their website and download their diagnostic tool to check the drive. If you don't know the drive brand, download HwInfo32 at hwinfo_com (_=.). Install HwInfo. Run HwInfo and it will tell you what brand of drive you have. Go to their website and download their diagnosis tool to check the drive. Their tool will tell you if your drive is functioning properly. If it shows that the drive is failing then you will need to replace the drive.
If the noise is coming from the power supply you will know. If it is, this could also be a dirty fan blade or a build up of dust in the power supply. Since you really don't want to be taking the power supply apart, compressed air from a hose or can can help remove the dust. If cleaning the dust from it doesn't work you may need a new power supply.
When you use compressed air on a fan, whether from a hose or a can, be sure to hold the fan blades so it will not turn. The blade will spin much faster than it was designed to turn and you can ruin the fan.
Hopefully one of these ideas will cure you problem.
When cleaning interior fans, bear in mind that the fans turn at very high RPM and the blades must be very balanced or the fan will start running out of balance with noise and considerable extra wear. If you clean the blades, clean them "evenly" or just as well on all sides and all blades. One person reported only cleaning one side with some cursory wiping and immediately had a horrible noise as the fan spun out of balance. With the light fan blades and fast RPM"s, it doesn't take much dust to unbalance them.