You are 30.
No Family, pets or friends and no attachments besides a 6 month lease on a tiny studio apartment and a full time job that pays $56k a year after taxes.
No possessions besides your laptop, mobile phone, a guitar you can't play and clothes/shoes.
You have only $10k in savings.
You have mediocre programming skills.
What would you do to achieve financial independence in the next 10-15 years?
You've got food and shelter and clothing and a job, which is more than a lot of people can say. Now focus on being happy. Go out and be around people. Tune up that guitar. Get one of those pets that you don't have.
Level up in programming (or accounting or mathematics or surface-mount soldering or art history, for that matter) if that's fun, but don't think of it as some kind of necessary step in making more money. Frankly, taking steps to make yourself happier and meet more people may be just as likely to help you make money in the long run.
Get a project and work on it every day. Practice practicing. Read The Power of Habit.
Edit: After reading a few comments from people feeling sorry for you, I'm afraid I might have missed your call for personal emotional support. Sorry about that. But if you were not after sympathy, then my original post stands. Practise to improve your skills (doesn't have to be programming). Do lots of practise while you have so much free time. When family and friends (and pets) come around, you will wish you were family-less, friendless and pet-less. And don't feel sorry for yourself.
That sounds miserable - I agree w/ @onion2k about fixing your situation before you work on other things. Life is not short, it's quite long and you have a lot of years left. "No family, pets or friends" for the next 50+ years sounds like you would be getting the least out of life itself. Read "How to Win Friends and Influence People" and work from there towards a few more ideas about how you can improve your life and health.
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To answer your question: Considering you want to achieve financial independence quickly, it's good that you don't own much stuff, otherwise your stuff would own you.
I recently discovered the blog Early Retirement Extreme. There is a post [0] which gives the simple equation which must be true if you want to become financially independent: "your annual expenses < 3% of your invested savings"
Assuming you keep the same living costs before and after becoming financially independent, you will need to solve this equation:
living costs = SWR * ( income - living costs ) * ( ( (1 + ROR) ^ number of working years ) - 1 ) / ROR
where SWR = Safe Withdraw Rate and ROR = Rate Of Return. SWR of 3% is taken from [0].
Assuming you can get 10% on your investments and can live on 25k a year, let's enter some numbers and solve for working years:
25k = 0.03 * (56k - 25k) * ( ( (1 + 0.10) ^ X ) - 1 ) / 0.10
X = 13.7 years
Assuming 10% again, and working for 15 years, let's see how much you could have to live on:
X = 0.03 * (56k - 25k) * ( ( (1 + 0.10) ^ 15 ) - 1 ) / 0.10
X = 29.5k
So if you worked for an extra 1.3 years, you could bump up your living expenses from 25k to 29.5k, a jump of $4500 a year.
EDIT: I forgot to include the 10k you have already saved up. I would probably leave that out of the investments and keep in an emergency fund (keep it in your savings, and future savings would go straight to your investment account).
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[0] http://earlyretirementextreme.com/can-i-retire-young.html
[0] Cummuta, John. "The Myths & Realities of Achieving Financial Independence". Nightingale Conant. Retrieved on 14-Sep-2009