Ok.
I though my answer was kinda brief and unclear, and I really didn't think that smiley face was that big. So, I've decided to post in greater detail.
Front panel headers are something I have to deal with a lot in my hobby of 'frankenboxing' (taking chunks of various old dead computers and assembling them into something that can watch youtube).
Now, there are dozens of approaches as to front panel header configurations, but a lot of common ones. I'd guess yours is using one of the most common intel configs, as your diagram kind of looks like a usb header. I'll show you how figure it out.
All you need to do is make the right pins go to the right buttons and lights, the rest is just a simple puzzle. First you have to identify which pins want which lights and buttons. Then, you figure out which wires go to said buttons and lights. Then, you just move them where they need to be.
First, I went to postimg.org and uploaded some photos. Then, I added the pictures to this post using the fancy button up top of the editor. There should be a button somewhere to the left of my post that says 'show bb code' that can also provide useful info. Now to pictures.
This is a random header cable I grabbed as an example.
In my case, the missing pin on the right is blocked to prevent you from accidentally plugging it in backwards. I think this one is for a USB front connector, but it uses the same kind of pins.
Now if you look on your board's front panel connector, you'll see something that looks like this:
But it's really no different from something like this:
http://2.bp.blogspot.com/_4Z3q0-hnVtM/TTaLMvS-PRI/AAAAAAAAAD0/IRq_d2fzn9s/s1600/11-frontpanel-header.jpg
Now you'll note this example has a legend. I'm kinda thinking from the look of it that this is a gigabyte board, but that's not the point. If the legend isn't right there, it's probably still somewhere on your board. If you see something like FP1 but no legend, look on the board for a chart labeled FP1 that will have the info.
There are 8 pins you are concerned with, and really only 2 you need to get right. Also, mixing up the plus and minus doesn't matter with the buttons. It may with the lights (can't remember), but it won't hurt if you get it backwards and have to switch it.
Going back to our example with the color coding--
+PW- Power Switch ***THE ONLY ONE THAT REALLY COUNTS***
-RES+ Reset Switch
+HD- Hard drive activity light
+MSG- Never seen a case that uses it. Possibly for displaying post error messages on a numeric LED?
NC The pin that goes below the blocked pin so you can't plug it in wrong.
Note: There is no Power LED connector here. It may be the three pins above.
The right side is just for the speaker. I thin this may be the same layout as your top diagram, but no way to be sure without it in my hands.
So step one is to look at your board and find the legend so you can figure out which pin is which. Trial and error is also acceptable. In my experience, I've never fried a board just tapping away with a screwdriver at all the pins until I find the power switch pins. The two pins closest to the blocked one on it's row is usually a good place to start.
Here's a video of someone jump-starting a rig with a screwdriver to set your mind at ease.
Step two is much easier. Just trace the wires up through your case to the front panel to figure out what is what. Many fall into a common color code, but enough don't that I never bothered learning it.
Step three is to move the pins where you need them. First, here's some more pictures.
Use an exacto knife to lift the plastic tab holding the pin in place, then gently tug to remove it.
Finally, put the pins where they need to go.
If the header plug is not physically compatible, you can hang it over the edge and just tape up the last two pins. Or, you can just say screw the header plug all together and tape all of the pins. USE AS LITTLE TAPE AS POSSIBLE. It's a tight space, and you're just trying to prevent accidental bridging.
Did I cover it all? I hope so.
Post back and let me know what you got from that.