Learn Turkish: Bilgisayarın ekranı kapalı. - The computer's screen is off.

This is a definite noun compound. The owner (bilgisayar) gets the genitive suffix -ın to mean 'the computer's', and the owned item (ekran) gets the possessive suffix -ı to mean 'its screen'.

Why does bilgisayar take -ın instead of -in?

The genitive suffix follows 4-way vowel harmony. Since the last vowel in bilgisayar is a, the suffix must use the undotted ı, making it -ın.

I have seen words take -nın or -sı for this grammar pattern. Why are they not used here?

Those are buffer letters used only when a word ends in a vowel. Because both bilgisayar and ekran end in consonants (r and n), they take the standard -ın and -ı suffixes without any extra buffer letters.

Does kapalı mean 'off' or 'closed'?

It means both! In Turkish, you 'close' electronic devices or screens to turn them off. The opposite is açık (open), which is used for devices that are turned on.

Where is the word for 'is' in this sentence?