"I was broken' with a different preposition that does not state 'by whom,' would form the plu perfect tense, e.g. "I was broken with nasty words." The status is current (present); however, the past participle without a 'perpetrator' indicates that I WAS (simply) broken (the preterite tense).

What tense of verb is were?

Meaning - Were is the past tense of the verb are. Look at this example of were used in a sentence. Since were means the same as the past tense of are in this sentence, it is the correct word to use.

Were broken or were broke?

BROKE is an ADJECTIVE when describing a person without money. BROKEN is an ADJECTIVE when describing something damaged, not working, etc.