I would like to use another website's design in building my own. I have no intent on copying any of the code, but I really like the way it is laid out and the fonts that are used.
Is it illegal for me to use the websites design but write my own code for the site? The content will, of course, be different.
Let makes it easier. Install Wordpress and buy or use a freely available Theme on it. By doing that you won't be copying no one. And you'll be free of any guilt. Ohh, and you won't need to copy any code from anyone. Bonus point!
Best of lucks!
It's not illegal, but could be immoral or at worst illicit. Personally I think it's fine to draw heavy inspiration from something in the early stages, but the second you're making profits you should switch to an original design to avoid making money off someone else's work. At the end of the day someone paid for that design to be created, and no one else should reap the monetary benefits from that.
But as an early-stage startup to test the waters and gain a bit of traction I think it's morally ok, as long as it's not a >95% exact copy. Same layout and fonts is fine, but perhaps inject some of your own personality into it.
Look at the main html "container" structure of the site that you like. It is just a set of nested tags. With the browser's "view source" menu item you can inspect it and then replace their actual content by placeholders.
That core (layout) structure in itself is probably not copyrighted. It rarely is. You see, a composition of rectangles -- such as an html layout -- could indeed be copyrighted, but then it needs to be something like Mondriaan's "Composition with Red Blue and Yellow". If you change the colours in Mondriaan's composition, I seriously doubt that the nested rectangles would still form a complete copyrighted work. It is not thát recognizable ...
Next, you can find the list of fonts in the sites css files. Fonts can never be copyrighted. If they could, the font copyright holders would also control the copyrights of what is written in them. That was absolutely not what they wanted to achieve when they invented copyright. Therefore, do not worry whatsoever about the fonts.
Isaac Newton famously said: "If I have seen further it is by standing on the shoulders of giants."
Copyright adds a few landmines to that principle, but should not prevent you from learning from what you see around you, and extract particular elements for your own starting point. Happy composing!