How to make a NAND Gate?
Your circuit is a strange mix of upside-down-ness. Figure 1 shows a more-likely-to-work configuration.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The standard solution to this problem.

A few tips:


Draw your schematics with positive rail on top and negative at the bottom. It will be easier to trace current flow from top to bottom.
Draw inputs on the left and outputs on the right. (You did this.)
Add a ground symbol somewhere. Even if not connected to the Earth it provides a reference for all measurements taken on the circuit.