The Legend of Zelda
This area is quite empty; there are no enemies or items here that Link can collect. The only thing that Link can do on this screen is enter the cave to the top-left. Inside, the Old Man begins Link's quest by giving him his first Sword, telling him, "IT'S DANGEROUS TO GO ALONE! TAKE THIS". After this exchange, Link can exit the cave and begin his quest to save Princess Zelda and, in turn, Hyrule. Every time the player continues the game on a previously saved quest, Link appears on this screen.
BS The Legend of Zelda
BS The Legend of Zelda MAP 1 begins on a recreation of the original starting screen. The BS-X mascot (from a choice between male and female mascots, replacing Link) immediately and automatically walks to the cave to meet the Old Man, after which control is given to the player. This repeats in subsequent weeks.
If the player has collected all the Triforce fragments, they can fight Ganon in a formerly-hidden room within the Starting Screen cave at the end of Week 4 (from the 45 minute mark onward) to save Zelda and the Old Man.
Four Swords Anniversary Edition
The added content for the DSiWare "Anniversary Edition" of Four Swords included a The Legend of Zelda triptych of levels in the Realm of Memories. These used parts of the actual map of the game, rather than randomised areas, and the first The Legend of Zelda-based level begins on the original starting screen.
In this version, the door leads to a tunnel which a Link can pass through, unseen until he emerges from the other side of the rock, rather than a cave with the sword.
Starting Screen on the Nintendo Switch Online "SP" edition of The Legend of Zelda