There is no guaranteed or proven reason to why you were banned it could've been caused by a variety of things such as not being careful enough and using homebrew applications while online, using a shared console id, playing games without antiban, console reports, suspicion from holding so many accounts on one console.
Like I said there is no possible way of knowing why or how you were banned but firstly I suggest you get a new console, scrap all your accounts and for your most important accounts (ones that have purchases etc) ring sony and say they were hacked or something.
I would also suggest changing your PSID (use ccapi and find a PSID from a youtube video or some shit, people forget to cover them up but they aren't worth a cent unlike CID's (Console ID's)), Since Console ID aren't allowed to be sold or distributed on this site I suggest moving to another forum and asking around (I'm not allowed to name the forum names as it's probably against the rules) however try asking around on skype and I'm sure you can find someone selling Console ID's, the prices range from $10-20, I wouldn't pay anymore then $20 for one as you're not guaranteed it's "private".
Good Luck
P.S There is no need for a firmware change or the use of PS Ninja / PSN Patch, simply play it safe... you can find plenty of threads which have proven methods of making your console and your accounts last longer, I highly suggest you make fresh accounts which you have no care for if they get banned or if they survive and use them strictly for modding purposes on a modded console as you don't want to put your retail console at risk or anyone else's (if you have one)