Wordpress does not properly display CSS file

Wordpress does not properly display CSS file

I have a crazy problem happening and it is blowing my mind. I installed
Wordpress on my Localhost and began developing. I modified the standard
twenty twelve theme and add custom HTML and CSS to the whole site (4 or 5
pages.) The site shows up great on my local machine (Mac OSX - Safari
6.0.5, Firefox 23.0. Chrome 29.0).
I transferred my site to my live host (under GoDaddy) and I migrated the
database by dumping it and then importing it. Now I can pull my site up
under both my localhost and by going to the live host URL and the site
looks exactly like it should. However, when I crosscheck the CSS via sites
like (browsershots.org and browserstack) the site look terrible. Its
almost like the main style.css file is not being linked properly. These
browser check sites shows the site in ruins on all operating systems and
all browsers. Still though when I bring the site up on my personal machine
it looks just as it should. My client pulled the site up from their
machine and it looked in ruins, just as the css checking sites depicted
it.
I have cleared my browser cache thinking I may be reloading a cached
version of the site (giving me false hope that it looks good) however it
still appears just like it should while viewing the remote version through
my local machine.
Side note:All elements of the page appear to be loading fine. The menu bar
is there. The text and content is there. It's just not styled.
Does anyone have any idea what may be going on?