Infinite (The Infinite Quest)

The Infinite was a spaceship from the Dark Times.

It was said the Infinite was powered by an Old One and whoever found it would be granted their heart's desire. The Infinite crashed on the asteroid 7574B of the Ceres system. Its parts were scattered throughout the universe, and power within faded away. Four data chips were needed to find its secret location.

In the 40th century, these four chips were found by Captain Kaliko, Ulysees Meregrass, Gurney and Baltazar. The chips' carriers were murdered by Baltazar to enable him to locate the ship. He also used the Tenth Doctor and Martha Jones to learn the location and hijacked the TARDIS to get there. The TARDIS was essential for the quest because the Time Lord technology could read Dark Time technology.

The vessel did indeed have the ability to show people their heart's desire: it provided Martha with a romantic image of the Doctor and untold riches for Baltazar, but the Doctor prevented the vessel from showing his heart's desire. He then destroyed the vessel. (TV: The Infinite Quest)