Instead of complaining about your teammates being terrible and all that...
TL:DR Play a weird, unusual role for a champion, then try to win with everything you have. When you're at a disadvantage, don't blame others, but try to work with them. This is a team game, not a solo game, and everyone is in here to enjoy themselves, believe it or not. Some forget what playing too serious means.
...Why not try to play a fun game with some friends?
If there's one thing I learned in nemesis draft, anything can be possible if you know how to play with it. Rather than play the ultra tank shen that normal people do, I played shen as an assassin. I would both try to save other people and keep myself alive.
Sometimes people are boggled why they have losing streaks or that "their team sucks" or anything else like that. But think about this, just for a moment: If you played something that seemed completely unconventional, could you win? And the answer should not be "no", and not "maybe" either. Try to always think "Yes, I can win this!" So here's a little experiment: play a game with a general theme, or play all characters in an out of meta way. I don't mean play Urgot, or anything like that, I mean play them strangely. You're playing nami? Don't play as a support, play as the APC. Playing lucian? On hit lucian could be fun, right?
When I played nemesis in unconventional ways, I felt I was playing smarter than when I play something "meta", such as an marksman as a marksman. AD shen wasn't just "try to kill them every time" early game, it was "work WITH my teammate to try and kill them." You can learn some valuable things when you play different roles in unusual spots, because instead of it being about winning the lane, then the game, it's about working TOGETHER to try and win.
This is all from personal experience. One thing many players do is complain that they have bad teammates, or they can't win games. Well, try to learn how to be a better teammate! Don't harass them, help them out. Don't try to surrender if you're losing initially, be patient. There are so many valuable things people overlook simply because they just want to win and head for the "best option", rather than what they feel comfortable with. Or, better yet, something they feel uncomfortable with. If you're forced to play something where you feel you're disadvantaged, most of the time you'll think of playing smarter and using anything you have to try and win, and anything means teamwork as well. Sometimes the most simple of things can be lessons.
I apologize if this seems like I'm rambling. I'm not an excellent writer, but I hope my message got through to the readers here. If anyone wants, I can attempt to play a game with you, with these strange conditions. I'm not great, but I'll try my best! So go on out there, and try something new. Refresh your league experience by doing everything the game has to offer, not just what "professional players do." See if you can get a little more enjoyment out of league.
Remember, league is nothing but a game. If you take it too seriously, you may forget what the meaning of "having fun" is. Plus, you could improve! Learning how to play with all of your strengths is something that will help you play the "meta" roles as well!