More detail is needed please. We need to know what make and model of computer you have, what are its specifications/components if it's not a Brand name PC, what Windows version you're using.

We'd also like to know if this is a new problem or if it's happened since you got/built the PC. What you were doing on or to the PC in the period before you first noticed the behaviour would help as well.

I have a Gateway, E-3600, I am using XP Home, SP 1. This has been an ongoing problem for about 6 months. Just like I said, it happens when you shut the computer down. You can hear the fan running and I have to unplug the power cord from the back of the computer. As soon as you plug in the cord it starts up immediately. The computer runs just fine otherwise. What do you think? Thanks for your reply..

when you shut down the comp and you hear the fan running does the power led lights still on? or just the fan on? and which fan is it?

No the power led light is not still on, just the fan. I think I only have the one fan in my computer.

Open up the system, and see if there are any lights on the motherboard. You might need a motherboard replacement-- it sounds like the BIOS isn't shutting everything down that it's supposed to.

Unless there's some really big current draw on the motherboard, you're probably not going to hurt anything, IMHO. If all else fails, you might be able to replace that fan with one that runs off of a drive power connector, unless you've got a system where the BIOS complains about not having a fan connected to it.

My fans keeps running when i plug in my emachine T1742 model
when it shut down or plug in it keep running.
I just replace the Power supply

Very simple. Your fan is intended to cool the circuitry to avoid permanent heat damage. If your fan won't stop running, it's because the temperature inside the computer case is constantly above the fan trigger because your vents are clogged with lint (trust me). Because the vents are clogged, the fan is blowing the hot air all around on the inside of the computer case instead of blowing the hot air out through the vents, so it doesn't cool down. Take off the computer panel, and use a compressed air can to blow the lint out from the vents near the fan. Some computers have more than one fan, so clean all of the vents. Make sure you blow the dust OUT of the computer so it does not end up covering other parts of the circuits. After you do this, your computer will run faster, won't lock up, and be very quiet after that.