I've got to admit, I've slightly lost track of what you're trying to do now. I was under the impression you'd got the search box to work using the code I put in earlier, which is basically Lynne's without the formatting.
If that's the case, then you need to start with that as a core and work your way through styling it how you want, just as with normal code. If you're putting it to the right of the postbit controls (the Post Reply button nasically) then it'll probably need to sit in <td> tags. The <form> tags, I think, will have to go outside of that. You may then find you need to make the <td> that the Post Reply button sits in have a width, otherwise it will spread across the page and push your search box over.
If on the other hand you want the search box on a different line to the postbit controls, none of that is needed.
The blue background must be coming from the background class it is sitting in, if you put it in <td> tags try adding a class such as alt1 or even page.
This is probably going to boil down to you posting a screenshot of your page, highlighting where you want the box, and then posting that part of your SHOWTHREAD template so we can give some pointers as to where to put it.