I have a child without being married and just found out that his father gets social security or disability due to illness like diabetes, health issues.. he has paid child support in the past, but stop paying since 2004. Also the birth certificate has my boy has my last name.

Which one is he on - SSi or SSDi ?

It makes a huge difference.

The issue is not that he doesn't have to pay support, the issue is that he may not have any income to pay support with. Some forms of SS payments are exempt from attachment, so if that's his only income, then there is no way to collect support from him.

Has child support been ordered by a court? If so, what have you don to try and collect?

(Note: Any question on law needs to include your general locale as laws vary by area).