In special relativity we say that a particle traveling at the speed of light uses all its energy to do so
Where did you hear this? A particle traveling at c can have any energy, but can have no mass. (E=pc)
ie (movement through time)
I think that this is a bad interpretation of the physics involved. One can not assign a co-moving reference frame to a particle at c, as c must always be c from every frame. Hence, no proper time can be defined (proper time is time as seen from a certain reference frame). This is not due to lack of energy.
This begs the question; what is giving the string the energy to vibrate?
Strings are quantum objects, and as such classical physical concepts of energy don't apply to them. Energy becomes an operator (as does anything we can
observe*), which is applied to a quantum state. It's corresponding so-called eigenvalues are what we measure as energy, which are quantisized. This means that they can only appear as products with integers. (e.g, you could have an energy of 123.3 Mev and 154.13 MeV but not anything in between). An interesting consequence of this is that a quantum system has a minimum
non-zero energy. So strings have some 'vacuum state'. (EDIT: Not to be confused with the ground state, which is the minimum energy in typical quantum mechanics). They can also gain and lose energy through various interactions. These interactions are governed by the laws of quantum field theory.
*A very important concept in quantum physics
Or does its maximum vibration equate the speed of light?
I don't think I understand the question. Vibration is not a physical quantity, by itself. We could define frequency, for instance. But not compare it to speed. If your question really means "does the speed of light 'barrier' apply to strings", then the answer is yes.
