This was me at the beginning of this season, though I found a great deal of personal fault in it as well. I started at Bronze II and climbed to Bronze I, then endured 6 (count them, S-I-X) promo series to try to break into Silver. After my sixth series loss I went on a pretty hard spiral and decided that I needed to do something different. The way I broke the streak? I stopped playing ranked completely, focused all my efforts on perfecting my game in normal draft, and then focused on teamplay.
What I learned primarily was this: no matter how well you play individually, if you are not helping, directing, or uplifting your team, then you are not contributing to the victory. Even in solo queue, the solo hard carry style just doesn't really work well anymore. It is much better to have a team that is (at least) halfway coordinated, understands the incredible value of vision, and has some basic knowledge of the aspects of teamfighting. That's not to say that individual success at any stage of the game won't contribute to a win, but it is to say that you must understand how to leverage your advantage and to share your success with your team.
Be persistent. Always find the takeaway and if you feel yourself starting to feel negative (or start to actually fear clicking the Ranked Queue option, as was my case), just do something else. Practice last hitting / freezing /pushing in a Custom, run an ARAM, practice a different role in Team Builder... just don't go into Ranked with a negative mindset. This above all else has helped me personally.
I wish you luck in advancing!