I used same process as I have with multiple other live distros on a Thinkpad.
Look at the process for downloading and burning to disc here: http://www.knoppix.net/wiki/Downloading_FAQ
If you did anything different, you might want to look there, for a solution to your concern.

How did you obtain your iso? Did you verify the MD5sums before burning? There are many incomplete isos on the mirrors right now and that will cause you grief when trying to boot. Did you burn the iso at a slow speed to compatible media of good quality?

You have given very little information for anyone to be able to help you. I have no clue where it stops booting, if there are any error messages, exactly WHAT hardware your ThinkPad contains, how old it is, how much memory it has, or what, if any cheatcodes you have tried, etc. They had a few more than just one model of thinkpads over a number of years.