Your debt is now owed to the third party and not to the original party. Do not pay anything to the original lender, as they have been paid (a much lower amount) by the 3rd party. You no longer owe anything to the original party.
With regards to your credit, if you have paid late, not paid, or defaulted and this is not in error, you can't really change what has been reported. However, you can clear up the remaining debt so that going forward, you will have a clean credit history. Over time, the old late/missed/default reporting will fall off of your credit report and you will eventually get back to a clean record.
Additionally, I think you will feel much better once the debt is paid. At some point in the past, you made a promise to pay for the service you received. By keeping that promise, you will be setting a new course in your life through responsible behavior.
Since you have a history of not paying the debt, you may also be able to settle with the new owner for a much lower amount. Try offering them whatever you have, even if it is 10% of the total. They bought your debt for pennies on the dollar, so they may be able to take a deep discount to the face value of the debt and still make money. They know than a high percent of defaults never pay, so they may rather take whatever you can offer instead of nothing.
Two key points here are (credit to Dave Ramsey):
1) Never give a collector or creditor your financial information, such as a debit card or account number. If you do, don't be surprised if they take whatever they can.
2) If you settle on a lower repayment amount, get the deal in writing before you give them a cent. If the deal for the lower amount isn't in writing, it doesn't exist in the eyes of the law.
And come back and tell us about your awesome credit in a few years!