Lucky you! All I would point out is don't you think that a multi billion dollar company might have had the sense to track ip addresses, otherwise what's to stop one user creating a hundred adsense accounts for fraud. All I would say is good luck as I've had clients banned over this issue. I won't even login to their accounts from my machine to avoid them or me getting a ban. One way they track banned users is via their ip. How the hell else do you think they do it, as anyone can use a new email and a fake address. Moving your computers ip is a little trickier. Also curious as to why you need to login to your clients multiple adsense accounts? Just I never have reason to check my clients adsense accounts. Only my opinion but I would say you are lucky but having seen the ip issue get numerous people banned, I still won't take the risk. If you happened to get flagged up over one account there's a high chance they'd ban every account logged on via your ip. Is that worth the risk?
OP. so you got banned from adsense. why? Did they give you a reason? Do you have any idea of how many people have had a second account that WASNT banned? I assure you, it would be a very low % of accounts that aren't banned. TCGG would be one of the few. Some people never even bother to fix the original issues, which means they are GUARANTEED to be rebanned (even if google doesnt know that its you) I KNOW you said you will open a new website, (not sure if you meant same content with different url), either way, most people seem to make the same mistakes the second time around. How much will registering a company take? whats the ongoing costs of running your 'company'? How much hassles are involved with doing all of this? And what if after doing all of this, you get your new account banned before payout. How much time, effort and money will you have lost? Bottom line is, your adsense account is gone, so just forget about them and move on with your life.
IP address is not reliable enough an indicator and I'd expect them to know that. Other factors will be taken into account.