I renewed my avast internet security a couple of weeks ago, and now I got a new computer for christmas. Is there any way to get my old avast to my new computer without having to buy a new one? Thanks and merry christmas to you all!
Yes, you should have saved the avast license file, license.avastlic, copy that to a USB stick and use that for the new system.
Uninstall the copy on the old system, that way you only have the 1 installation.
If you didn’t save the license file - Resend avast License http://www.avast.com/resend-license-paid.php, you will need to enter the email that you used when purchasing the license, e.g. the one that the original email with the link was sent.
A Merry Christmas to you too.
Uninstall avast from the old computer first, then download and save the latest avast to you new computer ( don’t install yet ).
Proceed to uninstall any pre-installed AV that has come with the new computer then finish up with running one of the removal tools from here http://singularlabs.com/uninstallers/security-software/ to remove leftovers, once that is completed you can install the downloaded avast from earlier and insert your license in the same manner you did previously from your email.
Sorry didn’t notice you had posted first David 
there’s some extra information here anyway for removing preinstalled AV.