Tesla coil troubleshooting help
A tesla coil is essentially a transformer with a really large ratio of turns, connected to a high frequency AC source. The problem with your circuit is that you're essentially, just letting DC current flow through the primary of your coil, which will not work. 

The simplest tesla coil design might look something like this (note, values are approximate, you should not attempt to build anything resembling this circuit without a thorough understanding of how everything works, and more importantly how anything can go wrong and KILL YOU)

How it works:


Initially, V1 charges the capacitor C1 through its output resistance (R1) until it reaches a high enough voltage to arc across the spark gap
When an arc forms across the spark gap, it momentarily shorts C1 to C2, charging C2 until the voltage across the spark gap is no longer high enough for a spark to be sustained
C2 begins to discharge into L3, increasing the magnetic field inside it as well as the current through it. When C2 reaches 0V, L3 still has a current flowing through it, so it begins to charge C2 up to a negative voltage, until the magnetic field collapses. At this point C2 begins to discharge through L3 again, and the cycle repeats until the energy stored in C2 dissipates due to resistance in the wires or losses in the transformer. C2 and L3 form what's called a tank circuit, which when given a pulse of energy, oscillates until the energy stored in the capacitor and inductor runs out.
The alternating current in L3 induces a high voltage in L4, making sparks and doing the tesla coil thing.







simulate this circuit &ndash; Schematic created using CircuitLab

The tank circuit formed by L3 and C2, and some way to periodically provide energy to it are integral to making a Tesla coil, you cannot build one without them.

Finally, as I said above, do not try to build this without a thorough understanding of how to work with high voltage. While the output of the Tesla coil is likely not deadly, C1 most certainly is.