OK you caught my interest
Does your dorm room window(s) only face one direction? (That's usually the case unless you're VERY lucky) If you have sun pouring in until late afternoon, then I would think your window faces south.... That's a good sign.
You should be able to grow most anything with that much sun if you supplement it with artificial light.
to consider: Large reflector clamp on utility lights (Lowes has them, probably other big box stores too) with CFL bulbs, 4' 2 tube fluorescent shop light fixtures (one warm, one cool tubes) hang with chain for adjustability or strapped to shelves (raise the plants to appropriate height), as well as securing the fluorescent light fixtures vertically on the wall.
What you don't have is the space. You won't have room to grow some things, and you'll also need to think in terms of productivity/sq. foot... (or more likely, sq. in.!)
The biggest issue here though is that you only have a limited time (until mid May? end of May?) to grow anything. So your best bet is radish, turnips, and fast maturing leaf crops. Look up "days to maturity" for SPECIFIC NAMED VARIETIES OF EACH VEGETABLE you want to grow. Off the top of my head, that would be mostly salad ingredients: earliest varieties of radish (28~30 days from seed), oriental turnip (25 days for greens, 35 days for root), baby swiss chard -- try Rainbow or Bright Lights for extra color) and mesclun (also about 30 days from seed), Chinese cabbage (30~40 days), leaf lettuce (40~50 days), beet greens (40~50 days), spinach (40~50 days, earlier for baby spinach), etc. These are all cool season crops, and if your growing area gets much above 75Ã‚ÂºF, they won't do so well (so RIGHT NOW is the time to plant them!)
Something else you can try is bush beans (about 50 days). I grew some bean seeds just for fun in 2L soda bottles (holes punched in bottom for drainage) and supported with a thin bamboo stake this winter. The runner bean didn't do so well, but the single bush bean plant has so far produced 7 pods. (It didn't need to be hand-pollinated to my surprise) It's sitting on a SE-facing double-glazed window with no supplemental light. Next winter, I'm going to plant a whole window sill row of 2L bottle bush beans
If your room gets very hot, you might be able to try growing cucumbers and tomatoes since there are some bush variety cucumber and EXTRA early tomatoes that mature in 50+ days, but you WILL have to pollinate them with a soft watercolor paint brush or possibly cotton swabs. People usually grow them in 5 gal buckets.
For the medium sized plants, cut-off 2L bottles will provide the extra depth and root space that most veggie plants need. (I suspect the clear bottle created the extra warmth in the root area that the bean plant needed too. This might mean cool season crops will not do as well with sun shining on the clear bottles when it gets warmer. Shield with a cardboard box, perhaps....). For small plants, lettuce grown in 16 oz and 24 oz drink cups grow bigger than when grown in same diameter flower pots.
Other plants to consider are culinary herbs and tea herbs (buy potted plants). Also, scallions and bottoms of onions cut in a generous pyramid root readily when bottom 1/2" is snuggled into the potting soil and grow green onion/scallions.
Search and read all the info people have provided in the Container growing forums as well as the various threads discussing supplemental lights in the Vegetable and Organic Gardening forums.
Oh, a final bit of advice -- use growing medium made of organic compost mix, potting soil, and sand (for extra weight so plants don't fall over). If you don't use chemical fertilizer, you can add a worm or 2 to each pot. They will make their own fertilizer. You can scatter coffee grounds on top of the soil (as long as it's fresh coffee grounds, your room will smell like freshly brewed coffee) and bury things like tea leaves and bits of veggie scraps in the soil. My bean looked like it was done after 4 pods, then I introduced a nice wriggly worm in the pot, and it grew 3 more pods.