Absolutely.... You can do it two ways...
1)Go to Jameco.com and buy the appropriate 2, 3, and/or 4-pin 0.1" housings and pins to fit the (I assume) standard 0.1" spacing headers on your motherboard. Also get the prper pin crimper (the pins listing SHOULD have the tool's part # listed) Then ID the individual conductors in the ribbon (what function, + or -, etc). Split the wires carefully, trying not to cut through the insulation. Look at one of the pins... Notice two sets of "wings". The inner set needs to crimp around bare wire. The outer set (on the end) needs to crimp around the insulation to provide strain relief (no big deal if it doesn't). Crimp pins to each conductor that you need to use (try to keep them all facing approximately the same way so you don't have to twist the individual conductors much. One function at a time, locate the conductors and insert them into the correct housing in the right order. Plug 'em in. You can of course get fancy with all kinds of shrink tube and all...
2)While you are at Jameco, get wire too.... Then simply replace the entire wiring harness with new stuff.... #1 is easier, provided the current length of ribbon is long enough.
BTW, all your power, reset, HDD LED, etc aren't in one header block? Most newer motherboard designs are now... If they are, you CAN use a single say 2x9 (18-pin) housing to make it into a single plug solution.
Well, I got a minute, so here are the part numbers:
Jameco Electronics
Housings: All on page 61 of the catalog under .100" Non-Polarized Connector Housings and Crimp Pins. Left side of page at the middle and bottom, one section for single row, one for double row. Some of the numbers are as follows:
2-pin - 100811 ($0.15/pc 10 minimum)
3-pin - 157382 ($0.15/pc 10 minimum)
4-pin - 100802 ($0.19/pc 10 minimum)
20-pin - 103229 (you can cut one row off this connector and have a perfectly good 2x9 housing too) ($0.15/pc NO minimum)
Pins: 100765 ($0.10/pc 10 minimum)
Crimp Tool: 159265 on page 130. ($9.95/pr NO Minimum) Actually, you can use 99442 as well. I have both and they always come in handy.
22GA stranded wire: (if needed): on page 67.
126084 - Black
126033 - Red all colors $2.95/100' roll
126076 - White
Though I always just use black for everything, and am just careful to hook everything up right.
Hope this helps...