Ignoring debts doesn't make them disappear. Even if your state's statute of limitations says the debt is too old to collect, you still owe the money. The effect on your credit score decreases the longer the debt sits unpaid. The debt may remain on your credit report after it's too old to collect, however, and that also hurts your ability to get credit.
An unpaid debt does the most damage to your score early on, when it becomes obvious you're not going to pay. As time goes by, if you pay your other debts on time and take steps to improve your score, the old debt doesn't hurt as much. Paying current debts on time is better for your score than wrapping up a six-year-old inactive account. Even if your creditor gives up on collecting, the debt stays on your credit report for seven years.
As long as lenders and credit-card companies can see the debt on your credit report, it can cause problems. Even after you've rebuilt your credit score, the fact you stiffed one of your creditors suggests you're willing to do it again if you have to. If you pay off the old account, it stays on your report, but lenders will see you honored your debt. Paying it off at last will contribute to improving your credit score.
On The Other Hand
If you decide to pay off an inactive debt, don't use half-measures. Making partial or installment payments won't do much to your credit score until you've completely settled the account. It also resets the clock: that is, if the statute of limitations expired, partial payment "un-expires" it, so debt collectors can pursue you for whatever you still owe. If you aren't able to pay off the debt completely and quickly, you're better off letting sleeping debts lie.
If you're having trouble paying what you owe, pay your most recent debts first. Not only do they hurt your score more, but creditors can still sue you to collect on them. Secured debts that give creditors a lien on your property are particularly important: if you default on them, you can lose your house or your car. All a collection agency can do for an unsecured debt is take your money.