Why do you believe this?
- "Me fail English." is considered to be a well formed construction, or that...
- ...adding a conjunction is important in determining whether "I" or "Me" is should be used.
It's just not the case that either of those are true in standard English.
While, in theory, you can have any rule you want within some sub-dialect, that would be a very strange rule indeed.
If you believe otherwise, you are tragically misinformed and miseducated.
Using "me" in subject context is, besides being wrong, a social low-class marker. It does not come naturally to English speakers; it only ever occurs through exposure to the misuse.
There are well-known phenomena like
https://en.wikipedia.org/wiki/Attraction_(grammar)
which can become conventionalized and eventually part of native speakers' intuitions even though they can be contrary to a more logically consistent or simpler understanding of agreement.
This is not even a theoretical possibility. There are no low-class markers that don't come naturally, because no one is going to make an effort to present themselves as low-class.
You are getting really disingenuous, now. Who are you performing for?
No it isn't. You'd never say "Me accused her". If you don't like the inversion its perfectly fine to say "I and Mel accused her", but using "me" for the subject is never correct.