A cold start is a start-up routine designed to reinitialize a deactivated warp engine by balancing its engines into a controlled implosion, that was first implemented by Chief Engineer Montgomery Scott aboard the USS Enterprise in 2266. Under normal situations, it takes at least thirty minutes to regenerate and start warp engines without a proper phase-lock. (TOS: "The Naked Time"; TNG: "Relics") For cold starts on more advanced 24th century starship, injector ports must be properly aligned for a successful restart. (VOY: "Human Error")
Prior to 2266, the cold start was only a theory, that according to Scotty, could only be proven by "a chance odds of 10,000 to 1...assuming we had a row of computers working weeks on the right formula." It was assumed that if done wrong, a starship would, according to James T. Kirk, "go up in the biggest ball of fire since the last sun in these parts exploded."
After discovering the intoxication of the water that killed the Science Group of the Federation at Psi 2000 and beaming over back to the ship, the Lieutenant Joe Tormolen, that was intoxicated, unwittingly spread the polywater molecule, and Lieutenant Kevin Riley, affected by the polywater, shut down the engines, diving the Enterprise out of orbit and in direction of the planet.
Scotty knocked Riley down and, via manual matter-antimatter combination, powered and activated the warp engines, saving the Enterprise. But because of the theoretical intermix formula used, which involved the theoretical relationship between time and antimatter, the engine power went off the scale causing the Enterprise to travel faster than is possible for normal space. This extremely high speed, along with the gravitational field of the planet, broke the space-time continuum and sent the ship three days into the past. (TOS: "The Naked Time")
In 2378, B'Elanna Torres attempted to do a cold start of USS Voyager's warp engines after their warp field was destabilized by the subspace radiation encountered in Subspace Munitions Range 434. When joined by Seven of Nine in engineering, B'Elanna claimed that they had failed for the "fifteenth time," possibly due to misaligned injector ports. (VOY: "Human Error")