What happens to PLEX if you change the CPU

If you can get Windows to run again, without having to reinstall it, then no.

If you have a hard drive/SSD to spare, you can move the plex data folder to it. This should enable you to get up and running quickly, even if you have to reinstall your machine.
Just make sure that all your media continue to be available under the same drive letters and folder names they are using now.

Here is the procedure to move the Plex data folder: