Most crucial hardware for brute force and data processing?

$10.5K is an unusual limit.

when you are wanting such critical processing power, all components become important.
in such a system, there will always be a bottleneck, you just have to decide where you are comfortable with where that ends up.

for example: slow CPU? - upgrade it, then memory is the limiting factor. upgrade that, then graphics is the bottleneck. get a SSD then you're back at wanting a better CPU. it's a vicious circle.

so to answer your question, it's the best of everything that your budget can afford.
and realising that there will always be better!

@Xavier Donnelly - any update?

no updates necessary unless you have further issues.
let's close this for now, and if you have further questions, PM any staff member to have the thread re-opened.

be aware - when you mention phrases like brute force cracking - alarm bells ring!