Apparently, your situation is different... had you been permanently suspended (a.k.a. BANNED for LIFE!) from Google Adwords alone for a repeated violation you can't get back in.
if u promote your websites against google adwords rules , u could be banned .if not any , you can contact them
I wonder how intense the ban is. Knowing google they can blacklist your google account, your IP...and your SOUL!
I don't know about applying new accounts for AdWords. But I do know that it's again their TOS to have more than 1 AdWords account.