I could just say "Everything is OK"

but that would be like reading the last page of novel without all the juicy parts.
So continuing from where the bookmark was:
If not, what is not working properly presently?
(I started making notes and don't want to waste them as I spent a lot of time so am posting my notes and Final Chapter..)
I will try to explain what I see when I open K browser.
I see the File Edit View etc. I seem to be able to use those OK. I note that when I go to Settings and see a menu that there are NO boxes to put a check into. Yet I can still click on an option. I mention this as I saw OP's have a check box.
I seem to show in the Settings that I have the Location and Search Tool bars enabled.
But I only see a big rectangular white space. While I can put the cursor in the box, I can not type anything.
(There for a while if I clicked in there and started to type, another box...half way down the page would appear....I posted a pic earlier.)
I have no Search box.
Now, I know before asking for help....some time ago, I tried to fix on my own so for sure I could have played with some settings. But it seems I would have played with the settings only in response to seeing it not work properly. If things were working properly I don't think I would have changed anything.
So what I can't do is Search or put anything into the address place. I could not paste an address there if someone gave me one.
HERE IS SOMETHING NEWI looked and it does show my HISTORY which still showed a lot of places I had visited. I decided to visit one via the History. When I clicked on a site it brought up the site...........
and also the Search Bar and the Address bar. SURPRISE.

I then closed that Window.......and it closed but the original Window without the Search and Address was still there underneath it.
The pic shows the 3 Windows Original, History and the Window when I clicked a site from the History list.

I closed out all three Windows and then restarted Konq and the Search and Address were there.

Whether it would have done this had I used the History before doing the suggested steps....I don't know. Maybe you do. For now it seems to work and you will be the first to know if it doesn't.
