The smartass answer is the correct one. Until you pay the old bills off, your score will not get better. Period. There is no magic bullet or miracle cure, anyone who suggests otherwise is full of sh!t.
My advice would be that if you can't afford to pay the old debt, you don't need a credit score at all. It doesn't matter if your score is zero. What you need to do is get on a written budget. Give every dollar of your income a place to go; spend it all on paper before the month starts, and don't spend one penny that is not on that piece of paper. That will identify how much extra money you have to clean up your debt.
The next step is to list all of your debts from smallest to largest. Pay every extra penny on the smallest debt, and pay the minimum on the rest, regardless of interest rates. Interest is not your problem; spending is. When the first one is gone, use that payment, plus the minimum you were paying on the second smalest, and attack that one. Keep doing this until they are all gone. Cut up all your credit cards and never borrow money for any reason whatsoever, except to buy a house, and you will never need a credit score again.
I get my paycheck in cash every week now, because I only have my truck to pay off. I have half of last week's check still in my wallet, which will go to the truck Monday. That will be two truck payments so far this month, and it's only the 10th. How would that feel, to have most of your paycheck left when the next one comes in?
EDIT: Using a debt management, or debt consolidation company has the same effect on your credit score as a bankruptcy. Those ads you see on TV from lawyers and debt consolidation companies, promising to settle your debt for pennies on the dollar, will reflect on your credit report in the exact same way as if you file Chapter 13 bankruptcy. There is absolutely no advantage, whatsoever, in using them. There are many disadvantages, like them not making the payments on time, though. They are notorious for this.
What's in my wallet? Cash!