Not having this. You were banned 4 years ago?
A public IP address is what everyone needs to get on the net. You used to be able to pay for your own, now you get them at random, think of it like a phone number, if you hosted a web page it'd have to stay the same. But you don't so you get one at random and they change a lot, especially when you reset your internet router as they aren't fixed (unless you do actually pay, business accounts only nowadays).
Now the ISP has to keep a log of the all accounts and IP address (phone numbers), and if you do something you shouldn't it'll come back to your ISP who will land you in the shit.
So, these are your options, you can either connect to a proxy.
A proxy is an address you put in your web browser, of another computer (you have either set this up yourself or are paying for it, there probably are free ones too). The proxy will go to web pages (and everywhere in fact) on your behalf hiding you IP and using the IP of the proxy and sending you the results.
Or set up a VPN.
A VPN is done on your network card, usually with additional software, it lets you connect to someone else's network (say your compaines), so you can work from home. Once connected, it is possible, (and usually the case) to break out from the internet, from the other location, using there public IP. The traffic is also usually encrypted between the two points. Meaning people who know what they're doing can't see what's in the packets of data you're sending down your internet line.
People will someimes use multiple VPNs, each tunnelling through to the next, and proxies too, making it very hard for them to trace.
Anyway, I digress. The only way you can still be banned is if your IP address has never changed (unlikely), you can check it now using
http://www.whatsmyip.org maybe restart your router and see if it changes. There is literally no other way IT way, I supposed they could run software to see if you type the same but that's unlikely :)
