You need to back up you database and copy that to the external drive. It’s easy and you should have done that on your old machine or whenever you are doing software updates and as a general good practice.
Import that into the new Resolve PC and just open up your projects. Make sure the external drive is using the same drive letter as it was on the old computer. You can always just open a project and it will tell you if media is offline and what the drive path was previously. Close Resolve, change the drive letter and reopen Resolve and it should all be connected