I suspect that particular model of EVGA is not among their good ones. It's possible that the PSU is starting to become a little flaky, and thus can manage with the integrated graphics, but is now struggling with the additional load of your R9 380.
Unfortunately, I'm given to understand that in Central and South American countries, high-quality PSUs are less available, and typically quite expensive.
Now I'm sort of not sure. It could be that the video card has died, or it could be that the PSU is not as robust as it once was (and it was never a strong model to begin with). I don't suppose there's any way you could borrow a PSU out of another system (if you have one) or from a friend, and see if your system works with the R9 380? That would help narrow down whether the card has died, or if the PSU is not aging well. Alternately, if you can try your R9 380 in another PC, in a friend's PC, or whatever, as an alternate method of determining whether it's really the GPU or not.
I know this is adding complexity to the problem, but I don't want to see a possible situation where you spend on another video card, then wind up with similar problems as you had with the R9 380.