Of these two options which one is correct?
Why doesn't the website get loaded?
Why the website doesn't get loaded?
Maybe the more natural one is:
Why isn't the website loaded?
but I'm wondering if either of the first two is correct.
Of the first two, the most natural sounding one is the first:
Although you will usually find it used in the active form:
When forming a question, the verb do moves to the front of the sentence.
As for your third option, that would indicate that you expect the website to have been loaded already, but it is not. It is hard to think of a situation where that sentence would sound natural, except maybe if you navigate to a website, go and get some coffee, and when you come back your screen is still blank. Even then, I think that these are more natural: