To address the original question of "Is Nikola Tesla's free energy discovery...", Tesla never created a "free energy device". One of his noted ideas, however, was a system to intentionally transmit power wirelessly. Power companies don't intentionally radiate energy (as it's a pure loss for them).
As an aside, Nikola Tesla was one of the first true electrical engineers, taking arcane, hard-to-understand forces and turning them into marketable solutions. While there is no doubt he was brilliant, this revolutionary engineer would quickly tell you that if you wanted to harvest naturally occurring electrical fields (not those he intentionally radiated) it would take an antenna (or an array of them) on a truly grand scale.
Regarding the document you linked:
Chapter 4 - Tesla's Radiant Energy Device
This chapter discusses a patent by Tesla which discusses using either the photoelectric effect via "ultra-violet light [...] and Roentgen rays [X-rays]" to generate a positive charge by ejecting electrons, or cathodic rays to capture electrons and generate a negative charge.
While you might be able to use the photoelectric effect from solar UV on metals, with great care, you are going to derive an extraordinary small current, certainly far less than you would get with a photovoltaic (solar) cell. PV cells use the photoelectric effect, but within a semiconductor.
Chapter 5 - The Tesla Coil
Tesla coils are essentially antennas that can radiate and receive a great deal of power. In order to actually capture an appreciable amount, much, much more must be broadcast on the particular wavelength that the coil is tuned to. Because they are tuned, they cannot capture broadband noise
To answer this properly, you should know the properties of a capacitor and an inductor.
Inductors are one of the primary components required by a switching regulator. A capacitor and an inductor are similar in the way that a capacitor resists a change of a voltage and an inductor resists a change in current. The "strength" of their resistance depends on their value
Capacitors are widely used to clean up a power supply line, i.e. remove noise or ripple at (higher) frequencies. Inductors are used in switching power supplies where a relatively constant current is passed through an inductor.
A switching power supply works in that a switch is opened and closed very quickly. When the switch is closed, the inductor is 'charged'. When the switch is open, the energy is drawn from the inductor into the load. Usually such a power supply is being decoupled with a capacitor to create a stable power supply line.
An inductor is required to make this principle work. If you know a resistor that has an equal resistance for all frequencies of signal, you should view a capacitor as a resistor that will be infinite for DC (0Hz) and 0 for high frequencies. An inductor will be the opposite: it's resistance will be 0 at 0Hz, and infinite at high frequencies. However we don't call this resistance (that's only used for a pure resistor!) but impedance.
A PC motherboard or graphics card is basically not much else than this. They have their main chips and the routing between them, and most other components are power supply or a little bit of interfacing between chips or connectors.
Best Answer
The magnetic field which stores the energy is a function of the current through the inductor: no current, no field, no energy. You'll need an active circuit to keep that current flowing, once you cut the current the inductor will release the magnetic field's energy also as a current, and the inductor becomes a current source (whereas its dual, the capacitor is a voltage source).
Aspects of the capacitor-inductor duality in energy storage terms:
\begin{array}{ll} \mbox{Capacitor} & \mbox{Inductor} \\ \mbox{* stores energy in electric field} & \mbox{* stores energy in magnetic field} \\ \mbox{* must be open loop (infinite resistance) } & \mbox{* must be closed loop (zero resistance)} \\ \mbox{* loses energy through parallel resistance} & \mbox{* loses energy through series resistance} \end{array}
A superconductor can sustain a magnetic field in a zero resistance current loop, however.
Unfortunately you'll always see the fumes of water vapor caused by the liquid nitrogen in pictures like this, which means temperatures below -183 °C.