If you are banned from Google then there is no way to convince them that mistake was made by some one else. This is what you can say is the drawback of a superb company Google that they punishes people for the fault of some one else.
u can signup for a new account with different payable name and different postal address info. but u can't place ad code at the ban site. Some ppl get back adsense ac and some don't (its up to google and depending on ur luck) How lucky u r??? Note: Now the matter is ur old site has pr , backlinks, traffic so u can contact adsense team and if they will not apporve ur application then u should place adbrite.com or peakclick. Now competition is tough tHERE r many other publisher prog. in the market which u can use. Try adbrite.com its knows as 2nd best choice after adsense & IF u r from usa then u can try yahoo prog.
I beleive they use Ips to see whos doing the clicking,and can get pretty close to the real location. If I did not click the ads myself, I would ask for a review on the grounds of the ip address. I have see several accounts be reinstated.
You can't get another account. One person can make only one account. I suggest you try adsense alternatives forums.digitalpoint.com/showthread.php?t=816484
You could make a new account with different name/id. Use your Sister, Brothers, mothers, Fathers, Your wife/husband, etc, and use another blog/website.