I recently took on such a venture and opted for PHP with the Phalconphp framework.

It worked out in the end (I did it over a weekend, not a whole week), but I have to admit that Phalconphp is not very stable - it's only at v0.4. But it is VERY, VERY fast.

The truth is that there is no way you can learn a whole language AND build an application in a week. So pick your favorite dynamic language and then find a lightweight framework for it.

My picks for lang would be in this order: PHP, Ruby, Python, Javascript (Node.js)