Firstly to help assist you we will need to determine the type of ban you have received. There are two (2) types of bans 1: Account bans (Can be temporary or permanent from a game specifically or psn all together)
2: CID Bans. If the CID (Console ID) is banned any accounts on the system will not be able to access psn due to the entire system being banned (CID's can be banned temporarily or permanently from psn entirely or a specfic game. 99.9% of the time thought CID bans are permanent. If you have been CID banned then you will have to obtain a new cid and change it on your system to get back online).

To find out what type of ban has been issued you need to verify if the account it self has been banned or the system entirely. To do this simply make another account on the console and try to access psn. If it deny's access to psn on a newly created account that signals your CID has been banned. If you are able to get online after making a new account then that means just the account has been banned. If this is the case you will no longer be able to ever use the banned account agian as sony rarely if ever lift's bans kindly.