So how can I say "My TV was broken by you", which one is correct?
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This falls under the difference between transitive and intransitive verbs. You are using the intransitive verb, when you should be using the transitive verb.
Transitive verbs require an agent to do them. They do not happen on their own, and need someone/something to do them. For example:
I woke Brian up.
I opened the door
Intransitive verbs happen on their own naturally. In other words, they are done automatically, without your help. For example:
I woke up.
The door opened.
There is a transitive/intransitive pair for the verb break. The transitive form is 壊す｛こわす｝and it means "to break." Because it is a transitive verb, you need to do the breaking, it does not break on its own.
You broke my TV.
The intransitive verb is 壊れる｛こわれる｝, and it means "to break, to be broken." This is a thing that happens on its own, and no one did anything to break it.
That TV is broken.
You are trying to say, "My TV was broken by you." This requires a passive voice, where the TV is the subject of the sentence. So you were on the right track when you used ～られる when you attempted this sentence. 壊す is a godan verb, so we won't use ～られる、but rather 「～base 1 + れる。」The conjugated form becomes 壊される。
Hope it helps.