I have an old hot mail account but I cannot access it anymore

It depends how long you did not access the account.
I know Microsoft changed a lot the last years and some time ago they warned everyone to access the account on a regular bases, because old accounts if not accessed for over a year could be solved and made free for other users.
Then the logon page has changed to. But you still can try to login on this page, Please put in the complete account name, with [email protected]. Don't forget the .com
Use this page:
Sign In

If you have an old Hotmail account and you cannot access it any more, you have to contact the Hotmail guys and ask them why your Hotmail is no longer operative, and they will do their best in resetting the account or giving you instructions to delete the old account and make a new one. If you have email addresses of family and friends, you let them know before making a new account because making a new account means changing your email address therefore you lose all your contacts. Find out first on what is going on from Hotmail. Send them an email and ask.

Through Microsoft, everything with access to Microsoft would be the same password, ID etc. on that account.
If your still not able to access then I would say your not able to because you don't have a back up email or phone or no access to that back up either. Then a call to them might help.