In its basic form, the circuit calls for a power supply, a large capacitor, the coil (transformer) itself, and adjustable spark-gap electrodes. Why these components, and what do they accomplish?

[Zach Armstrong] presents for your viewing pleasure a simple guide to building a solid-state Tesla coil. The design is based around a self-resonant setup using the UCC2742x gate driver IC ...

The coil was a standard 12V replacement and there is a ballast resistor in the primary circuit. The engine ran great until recently; it became hard to start and finally wouldn't start at all.