I'm sorry, but there are several issues, mostly with your writing sample, that are too glaring to be overlooked or let by with warnings for you to keep in mind while writing.
Most overtly, your grammar needs work. The only spelling error I found was "she dies her hair bright red", but both your biographies and writing sample (and some posts here on the Board, actually) are missing capitals, use numerals where they shouldn't, and there are a lot of commas missing, as well as some other punctuation marks. Some examples:
* 24 years old
- In prose, numbers this low should be written out: "twenty-four years old".
The following are all missing commas, which I have inserted to illustrate:
* Department: All-purpose Department, Star Trek Division
* to have to share his RC with a woman, mostly because
* Being from the north of England, he speaks with
* Shrugging decided to make a new message to kill some time.
- This should be: "Shrugging, he decided".
* from acting Captain of Engineering Joel of a nameless Federation star ship
- I've watched practically every filmed minute of Star Trek, and I've never heard of a "Captain of Engineering"; it's always been "chief engineer". I believe "Acting Captain" is a title that therefore requires both words to be capitalised, though that can be argued. Within the Star Trek world, "starship" is always one word, and I highly doubt it is nameless; all ships (save for Borg ones, I guess) have names (and Borg ships have designations). If he simply doesn't remember the name due to this amnesia, it should be very easy to look up, given that even if the computer were inactive and unable to supply the data, all Federation ships have name plaques on their Bridge. I realise this is supposed to be from an incomplete fanfic, but why couldn't you pick a name anyway?
* An event seems to have occurred where I do not remember the crew
- At the very least, "where" should be "which", but this sentence really needs to be rephrased to something like, "which has left me with no memory of the crew", or "that has caused me to lose all memory of..." Also, this seems like a very foolish thing for someone to announce on an open channel, given he doesn't know where he is and that there are pleanty of people even within Federation territory who would be quick to capture a lone starship with all its advanced and expensive technology.
* hadn’t used the words lonely or bored at all very professional.
- This really should be: "hadn't used the words "lonely" or "bored" at all - very professional." (though the dash, of course, can be replaced with a comma or even a semi-colon at will).
* (A few minutes before)
- Nothing technically wrong, but there is really no need for this, given how easy it would be for Sarah's diary entry to appear in italicised prose in the middle of the scene rather than before it. That is, of course, a matter of style, but if you insist on using this, I would strongly suggest having it italicised rather than in brackets, and that you use the word "earlier" rather than "before", following convention.
* “Excuse me can you tell me how to get to...”
There needs to be a comma after "me" and a question mark after the elipsis. However, since she is being interrupted, the elipsis should be a dash or a hyphen, like so: "Excuse me, can you tell me how to get to-?"
"Starfleet" is one word, with a captial "S" - it is neither "star Fleet" or "Star Fleet". "Star Trek" (referring to the fandom) should always be capitalised and (preferably) italicised. "World One" is a name and so both words need to be capitalised. There are a few other instances of missing capitals. You also have a habit of using the word "fairly" at every opportunity, sometimes in very close succession.
A good beta would solve most of these problems. However, I find it hard to believe that you could have missed the inconsistancies, if nothing else, which gives me the impression that you didn't spend a great deal of time on this, or even re-read what you'd written before submitting it. That is not exactly a point in your favour.
In terms of the content, I have no significant issues with your agents. They are somewhat bland, but have room to grow and a decent amount of contrast that could make for some good comedy. I'm more concerned by the blandness of the writing itself; simply put, there is nothing about your writing sample that is different from all the other partner-meets-partner stories around, and subjective though it is, you didn't make me laugh. To be fair, because we ask everyone to follow the same broad outlines there will always be similarities, but there was not one thing in your character interactions that will stick in my mind. This itself isn't grounds for denying Permission, but I want to mention it anyway.
A more minor point, but your bio says that Joel was from a fic that "was dropped before anything more than a character sheet was created." Offhand, I don't believe that a mere character sheet can create a character; I think it's the posting of a fanfic that enables it to affect the canon and enlivens it to the point that characters can be recruited.
Finally, you haven't exactly been the most active member of our community. Since your own introductary post, you've mostly just greeted other newbies. The other posts that you have made or replied to tend to be very short, contributing little to the conversation. When I came and saw your Permission request, my first thought was, "Who is that?", followed shortly by, "it can't have been a month yet, can it?" because I was under the impression that you were still a relative newbie.
So I'm sorry, but I cannot grant you Permission. I advise you to stick around, chat a bit more, make a point of continuing some conversations, and get a beta-reader for your re-write. Also, don't be afraid to give a little more description and depth to your writing; we're here to enrich the world of the PPC, not use as few words as possible to narrate a mission.
And last, don't be discouraged. You're not the first person to be denied Permisson, or even the first person I've had to deny. I hope you try again.