It's truly a mystery then.
I can apply any of the CSS I gave you in Firebug, and it works. Obviously, your frontend_custom.css is loading, and what else is in there applies. Like for example the style for the add-to-cart button, which is basically what's in template.css for *.art-button, plus what's for .hikashop_product_right_part input.btn.button.hikashop_cart_input_button in frontend_custom.css.
I trust that, whichever way you're accessing the server right now, you have write permission for the files, and changes you're making actually save.
What if you e.g. put // at the beginning of the line "background: -moz-linear-gradient(center top , #F500A3 0px, #AD0074 100%) no-repeat scroll 0 0 rgba(0, 0, 0, 0);" near line #2302 in frontend_custom.css and save? The add-to-cart button should lose the pink and turn grey. Does it do that? If not, you know you're either on the wrong server, or in the backup site, or can't write the file, or something else funny...