The Background info: (For the real question, skip to "The Real Question")

I rent an apartment with a small patio. I'm not allowed to plant flowers in the soil beyond my patio, because it doesn't belong to me, however there are large plants that have been planted by the landlord. They throw shade onto the patio almost the whole day.

The patio faces the south, and there is a brick wall (of a building) on the east side, and on the west, a vine-covered lattice. Because I have to pot everything, I tried taking the same type of flower pots that are designed for balconies and lining them up along the edge of the patio. I then planted the cheapest flowers I could find, and as to be expected, I was pretty unsuccessful.

My rose never even started to grow, my Daliahs are overgrown and only bloomed for about three days before all their petals fell off, my daylilies still haven't bloomed, but look like they've been trying to for the last three weeks, my Fuschia were beautiful for three weeks before suddenly dying, and my Geraniums (in a hanging pot) also very suddenly died, though their counterparts who sat unplanted in those little black cups you buy them in are blooming...

The Real Question:

Hence, I need some help. I'm looking for inexpensive, very low-growing (under a foot), colorful flowers that can survive in a small balcony-sized window box, in almost complete shade, in an environment which goes from being extremely dry and hot to quite cold and very wet from week to week. Winters are pretty cold, though it doesn't snow much. Forgiving flowers would be good, too, since I'm pretty bad about watering.