My Note does not starts, please help.

First I want to apologize if this issue is already treated in the forum, my English is not so good and I don't know how to find it. I will appreciate if someone can help me to fix the problem or to find the right thread.

The phone was working normally, battery was fully charged, then it started to change the bright of the screen and suddenly the battery was low. Some seconds after that the phone turned off and it does not start again. When I try Samsung Galaxy Note logo appears and then it turns off again. If I try recovery mode it doesn't start but I can put it in download mode if the phone is charging. (If not, a no battery message appears). Anyway, I cannot backup and I cannot use the phone. Android version was up to date and the phone was rooted. I would like to backup it if possible but if not I would like to tray a hard reset, but I cannot do this without recovery mode...

Thanks