Sorry I have not been available to answer your questions, but I am home and available now, should you still need any help.
To answer your current questions, first thing you are going to want to do is to check this image and see if it looks just like the part inside your Mac-min. The part is Apple Audio Board #922-7316:
http://applecomponents.com/items/922-7316board-audio/0000003035?pn=1&cmp=0095&perpage=30
You ought to be able to tell right away, as the boards do not look the same in the various models. (Please note, this is not the sound card, but is the actual audio board, by which the earphone jack and optical port are connected to your computer.) If this does look like the part inside your Mac-mini, then great, we are all set. If not, then let me know just which Mac-mini model you have, and we will see if we cannot locate the appropriate part for you.
To remove the audio board is really, really simple, but not, at first, obvious. Take your small Phillips head screwdriver- using a small flashlight helps anytime you work inside a Mac-mini- and look straight down from the top, directly at that small circular inset on audio board. You will find, to your surprise, I am sure, a single screw holding the board in place. Once removed, just rock the board in a careful downward and then out motion, being careful not to force it as the framework holding it in place is quite fragile. It should pull free quite easily, though, so you needn't worry too much. Once it is out, you can then simply reverse the process and install the your new audio board.
Be careful when you are connecting the new ribbon cable for the first time. Last thing you want is to crack it, right? So be sure to be careful and gentle. Also, if you look carefully, you will see a small brown plastic guard that runs along the base of where you plug the cable in. It is tiny, barely a fraction of an inch wide, yet is vitally important in holding the ribbon tightly in place. If you try to force the cable in place, especially by using tools, you risk popping this right out. If so, it ought to pop right back in with no problem, unless, of course, you lose it (it really is small), or else you break off one of the end pieces that snaps into place. Should this ever happen, you can still use it to hold the cable, but be warned that if it does ever break, should you upend the computer at anytime, you risk this falling off, even if your Mac-mini is closed.
If you have any questions, I am only too willing, now that I am home again, to answer whatever I can.
(Hey! I just checked Gainsaver, and they are now selling the audio board and cable separately, as well as together. Should your board still be good, and you only need the cable, you can get it there for under $4.00 ⚠. If you think you need a new audio board AND cable, you can get them both for only $8.99. (It has come down $10 in the few months since I bought mine.) While they are pre-owned, most places sell the same used parts for $40 or more. This is the URL address, to check out:
http://www.gainsaver.com/catalog/list.aspx?Keyword=%20Audio%20Board%20#922-7316
