how can I re activate my old apple ID?

If you deactivated your Apple ID, from the article below.

Can I reactivate my account?

Yes. If you request account deactivation, you'll receive a unique alphanumeric access code. When you're ready to reactivate your Apple ID, contact Apple Support, provide your access code, and we’ll help you reactivate your account. If you lose this code, we won't be able to help reactivate your account. 

Apple ID - How to deactivate your Apple ID account.    *

If you forgot the old ID, use every email address you can think of.

Apple ID - How to find your Apple  -  An iCloud e-mail address is an Apple ID.

Apple ID - Find  -     

Other ways to find your Apple ID

You can check if you're signed in to the App Store, FaceTime, or Messages on your iPhone, iPad, iPod touch, or Mac, or check if you're signed in to iTunes for Windows on a PC. You can also go to iCloud.com or appleid.apple.com and see if your Apple ID prefills on the sign-in screen.   

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option if necessary. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage  -     

Apple ID – Forgot Password  *