It's really very worrying that even when the visual appearance is completely different, we can still recognize a Template Monster template simply from the awful code that they write.
TM's original template has a quite a few problems structural and in terms of accessiblity (unless they meant to put a black search link against a dark grey background!). I'm afraid the structural issues are normal for their Zen Cart products. The ones to concentrate on are the DIVs inside LI tags as they could cause big problems now or in the future.
However a comparison of the original template with your current situation is helpful and points to the cause of the problem. You are missing two </div> tags to close the div with classes dt and 11 and the div with class dr nested inside that. As a result everything that follows gets erroneously swept up into this latter div pushing everything out of alignment.
With these div closures back where they should be, everything jumps magically back into place. But to do that on your site, you need to know where they have been lost from, and that's something we can't answer from this end, as we don't have access to the PHP that generates your site.
Either you have accidentally removed them when you suppressed the language and currency boxes, or Template Monster when implementing this template, put them in the wrong places so that you are forced to keep those boxes on preserve the header's structural integrity (which would be extremely daft, but sadly, entirely possible).