gestört
disrupted
Interrupted or impaired in its normal function, course, or calm.
Die Fernsehübertragung war durch das Unwetter gestört.
The television broadcast was disrupted by the storm.

disrupted / disturbed
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disrupted
Interrupted or impaired in its normal function, course, or calm.
Die Fernsehübertragung war durch das Unwetter gestört.
The television broadcast was disrupted by the storm.

'Gestört' (disrupted/disturbed) is the past participle of the verb 'stören' (to disturb/disrupt). It is used as an adjective to describe the state that has resulted from the act of disturbing or disrupting something.
Wegen des Streiks ist der gesamte Zugverkehr gestört.
Because of the strike, all train service is disrupted.
In this meaning, 'gestört' usually refers to technical systems, functions, or processes. Typical contexts are 'ein gestörter Empfang' (disrupted reception), 'ein gestörter Schlaf' (disturbed sleep), or 'ein gestörter Betriebsablauf' (disrupted operations).
Mein Internet ist seit gestern gestört.
My internet has been disrupted since yesterday.
When it comes to relationships, 'gestört' is almost always combined with words such as 'Verhältnis' (relationship), 'Beziehung' (relationship), or 'Vertrauen' (trust). It describes deep and often lasting damage.
Die beiden haben seit Jahren ein gestörtes Verhältnis zueinander.
The two have had a damaged relationship with each other for years.
When referring to people, the word has two registers. In psychology, 'psychisch gestört' (mentally disturbed) is a technical term. Colloquially, 'Du bist doch gestört!' (You're crazy/disturbed!) is a strong insult and should be used with caution.
Sein Verhalten auf der Party war wirklich total gestört.
His behavior at the party was really completely disturbed.
sick
'krank' and 'gestört' can both have to do with mental health or noticeable behavior. But 'krank' is also the normal word for being physically or mentally unwell. Colloquially, it can also mean 'crazy' or morally wrong in a derogatory way. 'gestört' more often describes behavior or a psyche that does not seem normal; as a label for people, it often sounds harsh and insulting. Learners may confuse the words because both are used negatively for behavior in colloquial language. For real illness, 'krank' is more neutral; 'gestört' should only be used carefully and in an appropriate context.

Der Patient wirkte stark gestört und brauchte sofort Hilfe.
The patient seemed seriously disturbed and needed help immediately.
Nach dem Wochenende bin ich krank und bleibe im Bett.
After the weekend, I am sick and staying in bed.