Hi,
The problem with that custom CSS you pasted is that it will hide all froms on every page. It needs a bit tweaking to hide the header on the front-page, but not on the other ones:
[html].page-id-14159 .asp-try-8, .page-id-14159 .wpdreams_asp_sc-8 {
display: none !important;
}[/html]
This will hide the header search instance on the front page only.