Shall I pay this six year old debt?

Do not pay this debt. It will do nothing for your credit score if you pay it. Each state has a statute of limitations on debt and your six years may be close to it or even exceed it! In Florida it's 6 years and in Nevada it's only 3! Do NOT tell them you will pay it or the time limit will start all over again. Find out what the statute of limitations is in your state, and if it is close or exceeded, tell them you are aware of the statute and to leave you alone. If the statute has run out and they keep bugging you after you have informed them, tell them you will seek action against them for violating the law.