Well, the style of the piece is important. Most of what you want is the presentation. I've done a few crime fiction pieces for exams, and I didn't even have time/room for the plot. So, basically, you need to work the delivery of it.
Develop a character - use clichés, if you like, or maybe some irony to parody the usual stereotypes. Creating an original character is probably too much at this late stage, so you'll want to follow the traditional structure. Tough name, such as Dexter Colt, Ruger Steele, Max Winchester..something like that - guns are good to use.
Usually, the setting is dark, noir-ish, with cigarette butts and half-empty whisky bottles, a poor detective sits at his desk, usually reading a newspaper and waits for a case, while he monologues/narrates in a dark and sardonic manner.
You may want to go with the traditional "dame sidles into the room" and asks the detective to solve her case, paying him a large amount of money, which he accepts out of sexual attraction and desparation for money/a case.
Two texts I would've advised you studying, if it wasn't so late, are "Dead Men Don't Wear Plaidt" (Steve Martin detective satire, very clever) and "Dirk Gently's Hollistic Detective Agency" (Douglas Adams' clever novel)
In any case, you'll want some heavy narration from the detective, and may like to throw in an interesting quirk or metaphor, if you can. I suggested to a friend that he has a visual impairment where he became colourblind from an accident, early in his career, which is a metaphor for his portrayal of justice (seeing things in black and white).
Anyway, start off with the run-down, feculent office and have someone approach him with a case, unless you'd like to stray from the original, and perhaps have him take a walk, or even start off with some action - driving off a cliff, shootouts, fist fights, drunken arguements - it's all good.
Eventually you'll want some intrigue into the plot, with twists, turns and suspects, but that may not even surface if you don't have time. Just make sure you have some snazzy presentation and your plot (especially if it is weak) won't matter as much. Though that's not to discredit the importance of a storyline, either. They'll want both.
Add humour if you can, as markers usually like that, unless you're going for a more hardboiled/gritty approach. Wikipedia also has some articles on detective fiction/noir, which may come in handy. If you get stuck, just give me a yell and I'll try to help you more.
Good luck,
Random Andy
