Wow, I totally could have written what you've said when I was younger. Sometimes I still feel that way.
First of all, have you ever been evaluated for ADD? There are some online tests that you can take to find out. Just do a search for ADD tests. I'll try to find the one from Dr. Amen's site. He is an expert on ADD/ADHD. The reason I'm asking you this, is because a lot of what you're saying sounds like you may have it. Not finishing things, not fitting in, even depression can be symptoms.
Second, I really want you to know that 15 is young. You've got your whole life ahead of you. I know that these feelings consume you, and you can't look past them, but please try. What you're saying scares me, because I know how you feel, and we've all seen the horrible things that can happen in these situations. (school shootings, suicide, etc. . .) I remember in 7th grade I was so horribly depressed and felt worthless (mostly due to some 9th graders who felt they had to continuously insult me and make my life hell). I didn't have the guts to do anything myself, but I remember wanting someone to just shoot me.
Now that I'm an adult, I realize that I have a purpose in life. I don't know what it is, but looking back, I can see God's hand in my life. I did some pretty stupid stuff when I was 19, and look back and think, wow, I could have been raped, I could have died, who knows what else He protected me from.
My point is that 15 is too young to give up. You said something about changing schools. Is this an option for you? Maybe you just need a different environment. People who don't know you. This isn't always the answer, but you could explore it.
I would also encourage you to find someone to talk to. When I was your age I didn't have a good relationship with either of my parents, so I never talked to them about anything. Find someone! Big Brothers/ Big Sisters? (don't know the age limits for that) Boystown hotline? Someone from your church?
Try to be more active. Volunteer somewhere. You'll feel good helping someone. Personally, I would love to volunteer at an animal shelter. Animals love you no matter what!
Most important, know that God loves you! I know that sounds cheesy, but think about the actual implications of that. The almighty creator of the universe loves YOU! Jesus died for YOU! If you were the only person on the earth he would have done that just for you! He loves you THAT MUCH!
If you EVER need someone to talk to, please don't hesitate! Even though I don't know you I CARE about you!