Who searched for but failed to find a westward sea route to China before Columbus?

Well, without doing any further research, I can offer that most of the European exploration before 1492 that had the specific intent of discovering new routes to Asia were carried out by Portugal. Most noteable of these exploits were those sponsored by Prince Henry the Navigator. There were many of these expeditions, under various captains, and they centered around finding a route to the Orient that went south and then east, around the Cape of Good Hope in Africa. Most noteable of these were Bartolomeu Dias (who was the first to round the cape before returning home) and Vasco DaGama (who successfully attempted to begin his course by heading in a westerly direction, and then taking advantage of the more favorable winds and currents to swing him around the horn). Dias's route was a crucial part in Columbus's planned course for his expedition. Now, if you are wondering about who else sailed west -- but not necessarily with the intent of finding Asia -- before 1492. There is a pretty good list, although a good many of them are not abundantly documented. Here are just a few names that I can get off the top of my head that you may wish to investigate: Saint Brendan, King Murdoch of Wales (that may not be spelled correctly), and Eric the Red. There is also evidence that sailors FROM China reached California prior to Columbus's expedition.