Yes, the previous respondents have pretty well covered the multiple issues that are causing your non-performance. Your main two problems are your transformer and your capacitor, AND your spark gap! Ok, that's three.
As has already been mentioned, a microwave oven transformer can provide a very lethal dose of amperage, to the tune of around 500 to 1000 mA, but only around 2000 volts, which is just too low voltage to reliably fire a spark gap driven Tesla coil. An old, iron cored style 12,000 volt, 30 mA neon sign transformer - NST (without GFI protection) is your best bet to get your coil up and running.
Microwave oven capacitors are only designed for maintaining a constant voltage and are used to double the 2000 volts from the transformer, along with a diode, to about 4000 volts DC to power the magnetron. They are NOT designed for the rapid pulse charge/discharge cycling of a Tesla coil circuit and as previously mentioned, they will quickly suffer a spectacular death if used as the primary capacitor of a Tesla coil circuit. You should look into some Cornell-Dubilier 942 series snubber capacitors to build a multiple-mini capacitor (MMC), or build yourself a homemade capacitor, or possible look into finding a surplus commercial high voltage pulse capacitor of the appropriate voltage and capacitance rating.
As for your spark gap, you are going to have to actually spend a bit of time and money to design a reliable and reasonably faultless gap. Google up "RQ spark gap" or "Sucker spark gap" to get some design ideas.
Finally, I would strongly recommend doing some further research into Tesla coil design. Google up Richie Burnett's Tesla coil page and sign up online for the Tesla Coil Mailing List (TCML) and learn more about Tesla coil building before proceeding further, as this is a rewarding, but potentially very dangerous hobby!