Your lack of precision and failure to provide comprehensive answers to very basic questions from those trying to help you is
  ... uh,
    ...ummmm
      ...challenging!

Nonetheless, one thing I can say with some confidence is that the code at line 004 in what purports to be formmail.pl,

004:   $emulate_matts_code= 0;

strongly suggests that you are NOT using the formmail which at least two of us condemned. Then, line 018,

018:   $style             = '/css/nms.css';

makes it clear that you are using the NMS enhancement, albeit without the allowed customization (" From you@your.com" !?! )

Ah... you noticed "purports to be?" Well, what you've posted is not and cannot be the complete script, formmail.pl. It's not even a complete begin block (no closing }. As it stands, it won't do anything. So let's try that part again (... or not! See below.)

As to the html, I count at least 25 violations of the 4.01 standard -- most of which -- admittedly -- will be tolerated by many browsers. But the lack of a </form> and incorrect commenting are substantial... and make me wonder how you can tell us that this works.

Another statement -- this one made with considerable assurance -- is that line 004 of the html:

<form method="post" action="/cgi-bin/formmail.pl">

indicates that the working cgi-bin (that is what you posted, isn't it?) is in a directory directly subordinate to the root dir for the site "stonebeads.com" ¹. For lack of definitive information from you, I will premise this reply on one possible apache configuration,

apache's data dir
|		
|-(stonebeads') httpdocs (directory)
|			|   |- index.html
|			|   |- "comments page" (file containing the table you posted)
|			|   |- other webpages ( .html, .pdf, etc. files)
|                       |
|                       |-cgi-bin (directory)
|		        |   |- TKI.pl
|		        |   |- formmail.pl
|		        |   |- other cgi executables
|                       |
|                       |-css (directory - location is per formmail.pl fragment)
|                       |
|                       |-other stonebeads.com directories
|
|-other apache user (site) dirs (possibly)

Now, can you provide us with a similar diagram accurately representing the relationships among Apache, stonebeads.com, and your subdomain?

Your statement, "I have the formmail in the cgi-bin prior to my shopping cart..." also needs clarification. If you are describing the order in which formmail.pl and TKI_cart.pl appear in a directory listing, rest assured, that is utterly irrelevant (unless it points to a capitalization error on a system (*n*x for example) which is case sensitive (unlike 'doze). But I have failed to imagine any other reasonable interpretation.

"...the form on the new site the browser says the link appears to be broken, I get no server error messages." also boggles my mind. I'm guessing that the first part, re the browser, means you're getting a 404 error. If so, you should also find that in Apache's error log, the place to which I would expect "no server error messages" to refer. So explain that too, please.

And if you're merely trolling, my congratulations (or something) on taking me for a ride... but even a slow-Monk can learn (or run out of patience)... and I won't be responding further to this unless the quality the information in your postings improves.

Update: Duh. So carried away I forgot to write the footnote...

¹: Subordinate to a directory with user-accessible html, as opposed to the site's root dir, one level above the user-accessible html, or -- as some providers organize it -- as a single cgi-bin above any site's user-space directories.

Update 2: Fixed (I hope) ASCII art of hypothetical dir structure.