If, according to relativity matter is energy condensed, Wouldnt breaking open the endless "russian dolls" of matter to find the most fundamental particle which gives mass to matter be fallacious? Fallacious in the sense that searching for a particle composed of energy, energy being something immaterial forming the composition of matter, is searching for something that in itself has no physical existence therefore breaking down particles into sub-particulate matter would go on ad-infinitum because there would be no such "particle" to be found. Would it stand to reason that Energy gives mass to matter?
Ex falso quodlibet.
Relativity does not say that matter is condensed energy. Rather it says that mass (a property of matter) is equivalent to energy (also a property of matter). Given that matter has other properties which are not equivalent to either mass or energy (like electric charge or spin), it is quite obvious that that you cannot equate matter with mass.
Since relativity doesn't say what you think it says, your conditional has a false premise, and therefore you cannot conclude anything from it.
Note that also your assumption that the Higgs particle is the most fundamental particle is, according to current theories, wrong. It is neither more nor less fundamental than e.g. the electron or the Neutrino. For example the electron cannot be made up of Higgs particles because anything made of Higgs has neither charge nor spin.
Maybe you're confused because of the nickname "god particle" for the Higgs particle. In that case, you may be interested to hear that this name was the invention of a publisher who didn't like the originally proposed title of the book which coined the name: "The goddamn particle".
But relativity is in no way threatened by the Higgs mechanism: Mass is still equivalent to energy; it's just that with the Higgs mechanism that energy is an interaction energy with the Higgs field, rather than a separate type of energy.
This really would have been better under Physics.
First, let me clear up a few things for you.
Relativity has nothing to do with the energy and matter (specifically mass) being the same thing, beyond both coming from Einstein. Special and general relativity are theories dealing with the question 'what happens when you move at speeds nearing the speed of light'. The famous equation E=mc2 has nothing to do with that, and in fact specifically only applies when the object is at rest! To be completely accurate the formula would need to include a term for momentum.
Energy is not, by itself, a distinct thing. There are numerous flavors of energy in the universe, including but not limited to sound, light, heat, kinetic, and potential energies. One can convert between energies fairly easily.
The Higgs Boson (the 'God particle') is something being sought not because it is a small part of matter or energy but because it, if it exists, is the particle that carries the force of gravity. Physicists are looking for it, in the hopes of learning why some subatomic particles have more mass more than other, very similar particles.
And using current tools, we have found some of the 'smallest' building blocks beyond which matter cannot be subdivided. Electrons are one of them, as are up and down quarks. One of the goals of colliders like the Hadron collider is to find out whether we are missing some yet or not.
There are two kinds of mass, inertial & gravitational. Inertial mass tells you has resistent a particle is to motion, gravitional mass tells you hard strong gravity pulls. It was a puzzle as to why these two kinds of mass were exactly the same. It was Einstein who used this equivalence to physically conjecture General Relativity.
Mass as condensed energy just means that energy can too be the source for the gravitational field.
The weak force is a gauge field, and as particles, the force is carried by bosons, which like all bosons are massless. But this would mean that the range of weak force is infinite; experimentally this isn't true. One then suppose that the boson must carry mass. The question is where this mass comes from.
Its comes from interactions with the Higgs field; and the Higgs boson is the interaction of these two fields - the Weak & the Higgs. As wikipedia puts it:
Your question is:
Its not mass for ordinary particles that has been conjectured and found; but those of the weak force. Ubiquitous - yes; but not the sole source of mass.
On, the whole; and despite the Higgs boson; this is still true (or its converse).
The resonance project has a possible answer to this http://resonance.is
Nassim Haramein focusses on the space instead of the non-space that mass and energy are. According to him there is a structure to space that follows certain geometries which are fractal i.e. all things are bound by these geometries so certain patterns always repeat.
For example phi or fibonacci or vortexes.
From this viewpoint looking for a god particle is nonsense since it's more of a geometric relationship vs an actual particle that creates matter and energy.
So it's a principle vs a thing. If that are opposites.
The nice thing about the principle is there is no problem with infinity. It can go all the way down and up. No need to search for bigger or smaller things unless you actually need them vs just looking for them to find an end which might not actually exist.