I am so sorry you are having problems with your computers. kindly let us know how we can help!
First off, you can clear up the LR activation records for your old PC -- you may refer to this Support article for instructions on how to do this:
http://support.brillkids.com/index.php/article/manage-activation-recordsWhen you're ready to install LR in your new computer, just go through the entire installation process in the same way that you did it last time. Your software, content files, and license keys will always be in your Account Management page, and these are also regularly updated with the latest versions!
If you have any other questions, let us know and we always happy to help!