how to make an object activated by a player to activate something else

for example, I pick up a key, and somehow that makes the door open up so I can go to it.

How does the player pick the key up and then the door opens

Do you pick up the key by walking over it? If so, then on player overlap key set door open; door open could be a boolean variable on the door; door.open=true. If you are picking up with mouse click or touch, then on key touched/clicked, set door.open=true. Then you have an event, player can only advance or door will only work if door.open=true.

What is a Boolean variable?

scirra.com/manual/73/instance-variables

scirra.com/manual/83/variables

A boolean variable can hold the value True or False.

It has its own set of conditions and actions.

Also

scirra.com/tutorials/933/how-to-code-doors-and-lock-logic