It sounds like you have been banned from the AdWords, program. They do not ban accounts, websites, IP Addresses, or computers, they ban people. You must be a different person, without any ties or connections to you, to open a new account.
It doesn’t matter why you were banned, you must find out why, and successfully remedy the cause, then ask for reconsideration, if it was something that was no fault of your own then you may get reinstated.
It sounds like you may have opened a new account without closing the previous account, which is a direct violation of AdWords policy. That alone is all it takes to get banned from AdWords.