I can't remember my old password.

See If you forgot your Apple ID password https://support.apple.com/en-us/HT201487to try to recover the needed password.

If you cannot recover the password or equivalently cannot answer the related security questions successfully, then see: 

Security and your Apple ID https://support.apple.com/en-us/HT201303

This document says “without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account.” 

So, you will not be able to remove the activation lock unless there are extenuating circumstances. Still you can try to get it removed using the support options below. Be ready to provide any additional information to Apple you think may be pertinent to removing the activation lock (e.g., the receipt for your purchase of the device with its serial number on it or the existence of a court order instructing Apple to assist in the provision of access to a decedent’s information from the deceased person's accounts  (see How to request access to a deceased family member's Apple accounts https://support.apple.com/en-us/HT208510).

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169

Get Support: We’re here to help  https://getsupport.apple.com/. Go through the options to find the best support option.