Anstor was looking over some files that had been sent to him previously. He scanned them, vigilantly, making sure that there were no mistakes. He was actually flabbergasted at the idea that the heads of the CIA would choose him, a mid-level worker to scan such high profile documents. But then, he thought, perhaps they chose him, because he held no bias about the topics the documents pertained too.

He sat in his chair, on the 5th level of the Amniplex Building, working on these files. As it was midnight, he was the only one there, and this gave him quiet, which by this point in time, he needed very badly. He veered his head to right, looking out the window, to see that it was raining. Being alone in the building sort of frightened him, but he eventually ignored this impractical fear.

-Don't need the "sent to him previously"

-Don't need the "vigilantly". Adverbs are evil. Try a stronger verb than scanned, which implies he did not read them closely, a direct contradiction to vigilantly. Maybe "studied" or "picked through them"?

-A mid-level worker? For the CIA? Or is this some sort of cast? In SF, people will wonder.

-"high profile" seems out of place. It may sound cliche, but the government actually uses classifications like sensitive, classified, secret, and top secret for information (and in that order of secrecy). And believe me, it takes forever and a day to actually get clearance to see those things. For realism, if you are curious, I know labs have two basic levels of clearance, L and Q, and that there are clearance levels above that, but they are shadier and only labeled by little-known symbols on your badge. If he gets sudden clearance, it had better be an emergency. And I highly doubt they'd leave him on a classified machine unsupervised. But then, your readers won't likely know this, so I guess you could leave that part, as it sets up the mood of the scene.

-By the last sentence, 1st paragraph, I'm wondering why you are withholding what the files contain. We are clearly in Anstor's head, so I expect to know what he knows. Fill me in soon, I'm annoyed!

-By the second paragraph, we KNOW he's working on the files. Don't need another sentence rubbing it in my face that I don't know what they're about.

-2nd sentence, 2nd paragraph needs work. Surely there is a clearer way to write this?

-Don't just tell us it's impractical. Couldn't we have some internal monologue where he tells himself he's being impractical?

I feel like these paragraphs are telling me the story instead of showing it to me.

I know my comments have been negative. Don't let them get you down! If you've been working on this idea for a while, I'm sure it has merit and that the concept of the story is a good one. However, from what I've read the style is too distant, too much telling vs showing and an unfair amount of withholding info. Don't talk about the files unless you are prepared to devote some space explaining them (well, Anstor's impression of them--no info dumps please!).

The vagueness of 'some' makes the first important sentence weak. Also, although not truly a passive verb combo, 'was looking' would read better as 'looked;' however, as apeiron noted, something like 'studied' would probably be closer to what you wish to convey here.

The second paragraph seems especially distant. Maybe give us some of Anstor's thoughts -- but only briefly -- about why he needed quiet, and why he thought his fear was impractical. Keep us inside his head.

However, I tend to agree that if the documents are not important to the story, it would be better not to place so much emphasis on them. Having them in the scene is fine, but the more they're mentioned and made to seem important, the more the reader will expect them to play a significant role in the story. They will be waiting for that moment to arrive. If it never does, they will find the story less satisfying than if there were a pay-off involving the documents.

There is a lot of repetition across these first two paragraphs, and they could probably be amalgamated into one paragraph by losing the repeated ideas.

Adverbs are not evil! They're just misunderstood...

The fact that only one person has said they were interested (and that after you begged) should tell you something about the first 13 lines and what they tell the reader about the rest of the story.

The first 13 lines should make people WANT to keep reading. If they succeed, then the rest of the story should continue to make the reader want to continue.

Okay, I just made that up by myself this very moment.

Your opening does have good elements, but they quickly get lost in the shuffle. And you are shuffling here. Various points have been mentioned. The thing about that is that they aren't just nits, they are general issues that will probably appear throughout your story. In other words, you are not ready to take the critiques you will get back if some people here read the story in its current form.