You cannot take tense from one language, apply to another language, and expect no change. Remember, there's no such thing as "pure past tense". What you're asking about is an English expression with an English past tense.
The Korean expression, "텔레비전이 고장났어요", expresses an event that has happened in the past: in fact, it's almost exactly like the English sentence "The television broke." Due to the nature of the event, when we say it, the most likely interpretation is that the television broke, and it stayed broken until now: so it is in a broken state.
However, given additional information, the expression could be used to mean that the TV had broken, but it isn't broken now. In both English and Korean:
텔레비전이 고장났는데 좀 전에 수리기사가 와서 고쳤어요.
The television broke, but the repair guy came and fixed it moments ago.
If you really have to clarify, then you can, as in these examples. (Note: as always, the English counterpart is rough equivalent.)
텔레비전이 고장나 있어요. = The television is broken (i.e., is in a broken state now).
텔레비전이 고장났었어요. = The television had been broken. (Either it's fixed now, or it is irrelevant now.)
However, just as an English speaker would rarely say "This television is in a broken state," you normally don't say "텔레비전이 고장나 있어요", unless there's a specific reason for it. (E.g., you don't know why it broke, but you just found that it is in a broken state, and you want to emphasize your lack of information.)
In most cases, simply say "텔레비전이 고장났어요": that would be enough.