
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.

damaged
Describes a relationship or bond of trust that has been damaged or is no longer intact.
Ihr Verhältnis gilt seit dem Streit als nachhaltig gestört.
Since the argument, their relationship has been considered permanently damaged.

disturbed
Not mentally healthy or strongly deviating from the norm in behavior. Colloquially, it can also be used as a derogatory term for eccentric or antisocial behavior.
Der Gutachter stufte den Angeklagten als psychisch gestört ein.
The expert classified the defendant as mentally disturbed.
'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
In a harsh colloquial judgment, krank and gestört can both be strongly derogatory. Krank pathologizes behavior more broadly or condemns it morally. Gestört attributes the deviation more directly to the person or their behavior and often sounds especially blunt.

Weil Tim die Hilferufe absichtlich ignoriert, nennen ihn manche gestört.
Because Tim deliberately ignores the cries for help, some people call him disturbed.
Dass Tim die Hilferufe absichtlich ignoriert, finden alle krank.
Everyone thinks it’s sick that Tim deliberately ignores the cries for help.