How to create a good short video with limited supplies and time
Start by throwing all the technical questions out the window. ALL of them. Don't ask about what cameras to use, which software works, or techniques. Change your mindset and think about your story. 

What is it that you're going to tell us about? Find a story that's based on solid collective-consciousness archetypes (read Joseph Campbell's "The Hero's Journey"; free, libraries). The reason that we still have The Odyssey &amp; Shakespeare regarded as classics (and not Pauly Shore films) is that they play into the stories that run through our common experiences as humans. Life, death, money, power...BIG topics. But whatever you find for inspiration, work on your STORY first. 

Note that I didn't say "Script". For me, a script implies dialog. Story...not so much. Film is a visual medium. How can you communicate your story in pictures only? Pretend sound doesn't exist. VISUALS only. How will you tell your story? Show, don't tell.

Once you have a SOLID, VISUAL story...that's when you inventory what you have. Resources, locations, people, equipment. For a cell phone camera, if you can't light it really well from a budget perspective, that means the you shoot using what Edison used in the early days of film. The sun. Your entire story takes place outside. Shoot in shade so there's not a ton of harsh shadows. 

Try to create a soundscape that AUGMENTS the story instead of telling it. Narration is evil. Avoid it at all costs. If you need narration, go back to step one. How will you tell your story with solid visuals?

Hell, a silent film just got a bunch of Oscar cred. Kick-butt sound that's not dialog will HELP your film, not tell the story. Record your dialog in edit, in a quiet room, direct into the computer. Google ADR and Foley to get some ideas.

Also, prepare for a slow process. In filmmaking, there's good, fast and cheap. Problme is, you can only pick two.

Best of Luck!