You want to change the computer and move the Trados Studio TMs and projects from one device to another.

To move the TMs and the projects you can zip them on the old device, copy them to an external hard drive, and paste them to your new machine.
Please don't forget to zip as the TM may get corrupted while copying due to its size.

The default location for TMs is:
C:\Users\USERNAME\Documents\Studio XXXX\Translation Memories

And for projects:
C:\Users\USERNAME\Documents\Studio XXXX\Projects