License?
You can only use your Free License on one computer at a time. So on the old computer, go to Menu > Help > License and deactivate. Then on the new computer go to Menu > Help > License and activate using your license key.
If you have lost your activation key, you can get a copy sent to the registered email address, by going to http://www.emclient.com/lost-activation-key
If you want to run eM Client on two computers, you will need two separate Free Licenses.