iMovie no longer works on my iMac since I installed Ventura

It would appear that as you have installed Ventura ( upgraded to Ventura ?) then your GarageBand and iMovie versions are no longer compatible with this operating system. This is quite normal so the next step is to upgrade GarageBand and iMovie to versions that are compatible with Ventura.

The normal procedure is to drag iMovie/GarageBand to the trash and open the App Store and then click on "your name " at the bottom left corner.This will take you to your Purchased page which is a list of Apps that are associated with your Apple ID, paid for or free.

Here you should see GarageBand and iMovie listed, amongst others.

Against iMovie and GarageBand you should see a download symbol or Get or something similar, so download.

You may well get a pop-up telling you that you cannot download the very latest version but will be offered the latest version that your Ventura can run.

Let us know if you have tried this procedure already.

It appears that you have bigger issues since you have the same issues with Garageband.

Have you tried to drag iMovie to the trash and re-install?