External DC Power

Is there any way I can use the power from one of my PCI slots externally from the case?
Cause I think there is a special adaptor for it.

I'm sure you can, but why would you want to do that?
If I were you I would buy an adaptor, cuz you can't draw much current from a PCI slot. (look at some of the VOODOO cards, they use an external adaptor for a reason).
Its asking for trouble.

BTW: Welcome to the forums.

I have a monitor cooler and I just wanted something that would turn it on when the computer started.

You can put a card in your computer that will allow you to control devices outside of your computer. This kind of thing is done all the time in industry & I'm sure that if you do some hunting around you'll be able to locate a card to do this.

Since you are only trying to control 1 devices (Monitor Cooler), it would be alot cheaper & simpler to plug the computer & monitor cooler into a power strip. Whenever the power strip is on, the cooler would be on.

If its a 12V Fan you could use a molex connector (The ones you use to power your HD, CD-ROM and alike, Yellow and Back wire=12V).
If you want it to look good, use a PCI slot backplate(?) drill a hole for a plug (the ones used on amplifiers) in the backplate, solder a male plug to the FAN, put a female plug in the Backplate (use a grommet!!!, you don't wanna short circuit something) and to be safe solder the positive lead to the middle of the plug(s).

If you don't understand what I'm trying to tell you, just ask and I'll do some painting.

what he means is make it look like this one:

http://www.3dcool.com/?module=product&sku=monitorcooler