Google Adsense bans a user from the adsense account only but not from other google services. So your brother can easily use his orkut account or blogger account with the same google id used for adsense account.
If you have a broadband connection which uses DHCP(Dynamic Host Configuration Protocol) then switch off your modem and switch it on again this will change your IP address. So google will have no clue if your brother used the same PC unless there are cookies in your browser. So clear up cookies and cache before you use your account.
If you don't have a DHCP connection but use static IP ask your brother not to click any ads on your blog or website as these clicks may be recorded as fraudulent on your adsense account. Also do clear cache and cookies before using the PC. This should help. However, I am not very sure what information does google keep track to check for fraudulence but Google does consider that you could be using a public PC. So you shouldn't be having a problem if you follow these tips. However, if you have DHCP connection you need not worry so much just clear the cache and browser cookies and change your IP. Hope you are less worried now. :)