Translation:They hate themselves because they did bad things.
Hmm, I see that in this sentence 'because' puts the emphasis on the action 'they did' and 'because of' puts the emphasis on the 'bad things', however I think their meanings are still parallel. I feel, in both of them 'them having done bad things' (as a single conceptual unit) is the cause of them hating themselves.
I am agreeing with you that they are both totally different in terms of grammar, part of speech etc. But I still think their meaning conceptually is completely synonymous (semantically). By that I mean I cannot think of a situation in which using the one sentence instead of the other would cause any kind of change in meaning. Can you?
There are grammatical implications though and the Turkish sentence would be different if you use "because of." Namely "Onların kötü şeyler yaptıkları/yaptığı için kendilerinden nefret ediyorlar." There are other ways to word this as well with the ablative case :) Just like the English sentence, you don't have a conjugated verb, but rather a verbal noun.
It is composed like this:
You need to put the possessive case.
kendi_m = myself
kendi_n = yourself
kendi_si = him-/her-/itself
kendi_miz = ourselves
kendi_niz = yourself(formal) / yourselves
kendi_leri = themselves
It is you wanted to talk about something they made, I guess this is fine, but it would be a little less common to think about it that say.
However, what you said doesn't mean that at all. What you said is actually an idiom in English that would mean "to make one's condition worse." :)