| Invalid clicks is a "catch all" term that they use, but it does not always mean that the publisher cheated. It can mean anywhere from clicking on your own ads, labeling the ads, inciting visitors to support the site and click on the ads, etc. First off, check your site if there is anything that can be construed as enticing visitors to click on the ads or labeling them other than the terms approved by the TOS
It will not be up to Google to show you the IPs of those who clicked or to prove you did something dishonest. Instead, explain to Google through email in a very professional manner that you never caused invalid clicks. Include in your appeal your logfiles to help prove your case.
You have to remember that the first responsibility of Google is to satisfy their advertisers, where the money comes from; and not the publishers. They need to protect the interests of advertisers at all cost. As a result, any clicks perceived to be less than above-board are investigated oftentimes leading to the cancellation of the account of the Adsense publisher.
Contrary to what you think, there is right of appeal. There have been many cases of publishers whose account was initially disabled but reinstated back into the program. Here are some threads from Webmasterworld.com of such cases:
http://www.webmasterworld.com/forum89/9886.htm
http://www.webmasterworld.com/forum89/5960.htm
Read these threads and learn from what these webmasters did to get their accounts back. I am sorry that this happen to you, but what you can do now is to just appeal to them in a very calm, rational and professional tone.
Otherwise, consider applying to other contextual advertising networks:
Yahoo! Publishing Network (currently in beta and available to US publishers only) http://publisher.yahoo.com/
Intellixt http://vibrantmedia.com/site/web_01a5.htm
Quigo Adsonar http://www.quigo.com/adsonarexchange.htm
IndustryBrains http://www.industrybrains.com
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