¿POR QUÉ existen PORQUE, POR QUÉ, PORQUÉ y POR QUE?

The simple answer is that while they all sound the same when we say them, they all have different meanings!

por qué – a literal translation of ‘why’ & used in the same way.
¿POR QUÉ dices que yo debería saber?
WHY do you say that I should know?

porque – a literal translation of ‘because’ & used in the same way.
Deberías saber PORQUE te lo dije.
You should know BECAUSE I told you.

porqué – translates to ‘reason’ & needs ‘the’ or a possessive – ‘el porqué’ = the reason.

Te lo dije y eso es MI PORQUÉ.

I told you & that’s MY REASON.

If used in the middle of a sentence to mean ‘the reason for doing something’, it must be followed by ‘de’ & then the full verb.

EL PORQUÉ de decirte es para que supieras.

THE REASON for telling you is so that you would know.

Or with ‘de’ but no verb
EL PORQUÉ de esto es para que supieras.
THE REASON for this is so that you would know.

por que
This is the tricky one, & to be fair we can perfectly happily live without it – & most people do!
It sort of means ‘for which’ & needs a reason or motive ‘for which’ something happens.

Para que supieras es el motivo POR QUE te lo dije.

So that you would know is the motive FOR WHICH I told you.

Here are a couple of examples from the RAE:

Están ansiosos POR QUE empecemos a trabajar en el proyecto.

They are anxious FOR WHICH (reason) we’ll start to work on the project.

Los premios POR QUE competían no resultaban muy atractivos.

The prizes FOR WHICH they competed weren’t very attractive.

Nowadays we’d more likely add the ‘article’ of the reason.

Están ansiosos POR lo QUE empecemos a trabajar en el proyecto. (‘lo’ representing ‘el motivo’.

They are anxious FOR WHICH (reason) we’ll start to work on the project.

Los premios POR los QUE competían no resultaban muy atractivos. (‘los’ representing the prizes)

The prizes FOR WHICH they competed weren’t very attractive.