With version 13, you can install the program on as many computers as you'd like -- but, once you log in with your Adobe ID and activate the program, it remains activated until you deactivate it. And you can only activate the program on two computers.
If your old computer died and you can't deactivate it, you'll have one other activation. If you need another and can't deactivate from your old computers, contact Adobe Tech Support and they'll deactivate it from your old computer for you.
Supplemental information specifics....
What is your program - Photoshop Elements or Premiere Elements?
If and when you need to deactivate Premiere Elements 13/13.1 or Photoshop Elements 13/13.1 on a computer to which you still have access, then in the opened project go to Help Menu/Sign Out. That Sign Out is the counterpart of Deactivate which is seen in versions of Premiere Elements 11 and earlier. Close out of there. Key to remember is that Deactivate is not the same as Uninstall which is a Control Panel/Installed Programs task if your computer operating system is Windows.
If you do not have access to the computer...it crashed and has trapped your purchased activated serial number there, then explore contacting Adobe Chat using the following link Contact Customer Care