There is no "ignition point" at which a star suddenly ignites. There is Maxellian distribution of velocities in colliding hydrogen gas, so sometimes some protons move much higher velocities than others (just due to the random nature of collisions), and can come close enough to each other (overcomeng their static repulsion - main obstacle to fusion) so that short-range nuclear force fuse them together with plenty of energy released. But fraction of such fast protons is exponentially small, thus the factor exp(-E/kT) in the rate of nuclear or chemical reactions. As temperature increases, you may see that the above exponent increases too, and dramatically. Therefore percentage of reacting protons rizes dramatically with the the rise of temperature T.

Even on Sun nuclear reactions proceed at extremely slow rate: energy production rate per same volume is millions times less than in ordinary candela, and even thousand times less than generated by (barely warm) human body at rest. That is what I call "slow" nuclear reaction on Sun (and not much faster on similar, and even on bigger stars).