This solution will be long in length. Therefore a lot of reading.
In essence I am typing out a motherboard manual, of a sort.
May look complicated. This is because I get very detailed.
If there is ANY area I have explained, that you do not fully understand, please post back in a Comment.
I will try to break it down, and/or use a different method of explaining.
1) Let's start with power cables from Power Supply, to motherboard;
HP Support > Pavilion p6610f Desktop PC > Main Support page,http://h10025.www1.hp.com/ewfrf/wc/product?cc=us&lc=en&dlc=en&product=4299342
Product information > Product specifications > Motherboard Specifications, N-Alvorix-RS880-uATX (Alvorix),http://h10025.www1.hp.com/ewfrf/wc/document?docname=c02560084&tmp_task=prodinfoCategory&cc=us&dlc=en&lc=en&product=4299342#N64
Looking at the photo of the motherboard, it is 90 degrees to the LEFT; in comparison to how it actually is mounted in your computer case.
(BTX form factor motherboard, and computer case)
I would also like you to scroll down, towards the bottom of the page; and look at the illustration of the motherboard.
This way we can compare the two together, as I guide you.
A) At the bottom of the motherboard is the connector, for the 24-pin ATX main power cable.
Yellow/White in color, 24 socket holes. (2 rows of 12)
This is a General example of said power cable, and respective connector on motherboard;http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain24
[Note* Color of power cable connector, and motherboard connector; does NOT matter ]
In relationship to how it actually sits on the motherboard, while mounted in Your computer case; you will find it all the way to the LEFT.
Note the Lock Clip on the power cable's connector.
Has a hooked end that goes over a TAB, on the motherboard connector.
When deemed to be plugged in tightly, and correctly; the hooked end will be Over the Tab.
Operates on the same principle as a see-saw on a playground.
Squeeze the top in, to release when disconnecting.
B) 4-pin ATX +12 Volt power cable.
Yellow/White 4-socket hole connector. In the photo, above the processor socket, and to the Right of the square Aluminum finned Heatsink.
You will find it to the Right of the processor, and Below the aluminum finned Heatsink; motherboard mounted in computer case.
General example of said power cable, and respective motherboard connector,http://www.playtool.com/pages/psuconnectors/connectors.html#atx12v4
Note Lock and Tab design, just like the 24-pin ATX main power cable.
Power for the Processor (CPU)
PU521 on Motherboard Layout.
That's it for power cables TO motherboard.
2) The front of your computer is the Front Panel.
Header; Rectangular small piece of plastic, that has contact pins sticking up.
You have 3 Black headers on the motherboard, a Yellow header (1), and 2 White headers.
This will become more self-explanatory, as we go on ]
To the Left of the 24-pin ATX main power cable's, motherboard connector; and to the Left of the ram memory slots; are three Black headers. (Photo)
(Mounted in computer case, To the Left/Top of motherboard)
The Orange connector you see to the left of the ram memory slots, is a SATA connector.
Looking at the Motherboard Layout, you will see it is SATA4.
To the Immediate RIGHT of it, is the Front Panel header.
The area of contact pins on the motherboard, that the Main wires from the Front Panel go to; is the Front Panel header.
Main wires such as Power On switch, Power On LED light, Harddrive activity LED light; and Reset switch.
On the Motherboard Layout, it is marked as J18.
You should have a cable coming from the Front Panel, whose plug on connector; matches this header.
Has 9 socket holes. 5 on one side, 4 on the other.
The missing pin in the corner, on the Front Panel header on motherboard; shows you which way the cable's plug connector, goes.http://www.findlaptopdriver.com/n-alvorix-rs880-uatx-front-panel-motherboard/
3) I do not know sir, what the long black header is to the left, of the Orange SATA4 connector, is. It is P17.
However looking at the length, you should find only ONE cable, and plug on connector; that matches it.
Should come from Front Panel. (IF it is used)
4) I do not know what the black header is, below J18.
(Again, J18 is the Front Panel header)
I believe with process of elimination, that the cable that goes to this header, will become readily apparent. (IF it is used)
5) There are Four SATA connectors on the motherboard.
SATA1 = Dark Blue
SATA2 = White
SATA3 = Light Blue
SATA4 = Orange
(Photo. Also compare in Motherboard Layout)
This is where a SATA data cable plugs in.
Your harddrive is a SATA unit. Your optical drive (CD/DVD drive) is a SATA unit.
The Harddrive plugs into SATA1.
The optical drive plugs into SATA2.
Any additional SATA units will plug into SATA3, or SATA4.
Example; A second SATA optical drive.
This is a general example of a SATA data cable, and SATA data connector on motherboard,http://en.wikipedia.org/wiki/File:SATA_ports.jpg
Note the SATA data cable connector. Has an L-shaped opening.
When connecting the SATA data cable to Harddrive, or optical drive;
Turn this L to the Left, and upside down. The 'foot' of the L always points DOWN.
Note the SATA data connector example shown. This is an OPEN design. Your SATA data cable connectors on motherboard, are a CLOSED design. Still has L-shape on motherboard connector, though.
The SATA data cable connector that goes to the Harddrive, and optical drive; is usually a 90 degree bent elbow.
NOT always though.
The SATA data cable connector that goes TO the motherboard, is a Straight connector.
Between a SATA data cable connector, and a SATA power cable connector; a SATA data cable connector is Shorter in width.
SATA data cable connector has 7-pins.
SATA power cable has 15-pins,http://www.playtool.com/pages/psuconnectors/connectors.html#sata
Same L-shaped interface is used.
Most of the time there is a Lock, on the SATA power cable connector. May be a Tab that sticks up, or a small lever, or a rubber 'bulb'. Depress with thumb to connect, or disconnect.
USB headers on motherboard, and USB connectors on motherboard.
Continued in added Comment.