The key point to consider has already been raised; the competitiion between the strong force and the electrical force. When particles are far apart (separations greater than around a fermi), the electrical force is much larger than the strong force. It is only when you get particles less than about a fermi apart that the strong force can overcome the effects of the electrical force and bind the nuclei together.
This, however, is no trivial exercise.
The electrical repulsion for protons one fermi apart is huge. The energy needed to overcome the barrier is on the order of
where the charge of a proton (c.g.s units) is 5 x 10**(-10) e.s.u.'s and 1 fermi is 10**(-13) centimeters. This energy is E ~ 2.5 x 10**(-6) ergs. For a gas to have particles with kinetic energies this large, the temperature must be 1.5 x k x T ~ 2.5 x 10**(-6) ergs or T ~ 12,000,000,000 Kelvins
The high temperatures required to overcome the electrical force is the major impediment to nuclear fusion in stars and on the Earth.
The key to this lies in some odd consequences of Quantum Mechanics. To get a feel for the effects, recall the Heisenberg Uncertainty Principle.
So, what happens is this.
Particles cannot overcome the electrical repulsion (classically) because the electrical force (hill) is too large. However, a small fraction of the time, particles can tunnel through the barrier and appear close together so that the strong force can bind the particles together. The shorter the distance the particles have to tunnel (the closer they are to the top of the hill), the greater the probability that they will be able to tunnel. As a result of tunneling, enough nuclear reactions can take place in the core of the Sun at the low temperature of 15,000,000 Kelvins!
Since hydrogen is the simplest element (1 proton), it has the weakest electrical charge and so has the weakest electrical barrier to fusion. Because of this, it is the first nuclear fuel to be used. Consequently, we know that the Sun is in the first stage of its nuclear fusion lifetime. After it uses up the hydrogen in its core, the Sun will be forced to burn helium, the next most complex element (2 protons).