Investigate the protable license utility. Set it up on your new computer, making sure you get the license name and identification code absolutely correct for your new computer.
You will need to set your acad up on your new computer first in order to get that data, then write that data into the portable license utility on the old computer, so the license can be transfered to the new computer.
Read up on this procedure in Help. BUT, and a big BUT. Be very careful, if you get it wrong, you are buggared.