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Moving to Premiere Elements forum
Welcome to the Premiere Elements Forum.
I constantly migrate my Premiere Projects between my laptop, and my workstation, but I set those Projects up, initially, with that in mind - which is different than having a Project set up on one computer, and then moving it to another. For my setup (remember, this is initially, when I start a Project), see these two articles:
For existing Projects, there are a couple of ways to address this. The method that you use, might depend on how you plan on moving the Project.
If you have an external HDD, and plan to use that to do the move, see the "Using External HDD's" article above, as it talks about drive letters in the OS. Getting that correct first, can save a lot of work later.
Then, one can use the Project Archiver to Copy the Project, and necessary files to that external. When one has done that, I strongly suggest that they test that "archived Project," to make sure that the Archiver has gathered everything necessary. The success of that process can depend on how one has set up their folders and sub-folders, and where their Assets (the material that has been Imported into the Project) is located. That is why I always urge one to test everything first. Then, just plug that external HDD into the new computer. At that point, they will have two options: edit to/from the external, or Copy everything to the new computer. For the former, see that "Using External HDD's" article, as there can be some limitations, such as both HDD speed and connection speed, that can impact how well things work.
Next, one could just Copy (over a a wired, or wireless network, or via an external HDD), the Project file (PREL), all Assets, and most of the Scratch Disk folders, to the new computer.
Note: there are files in the Media Cache, such as CFA's and PEK's for the Conformed Audio, that do not have to be Copied/Moved, as PrE will rebuild those (give the program time to do so, and do not edit the Project, until they ARE rebuilt). Same for the Render Files, as if those are needed, one can easily hit Enter/Return, to Render the Timeline, or part of it, again.
Keep the folder structures.
If one gets the "Where is file _____ ?" message, this ARTICLE will be helpful.
Note that the PREL (Project) file is really an XML database. It contains NO MEDIA, but only absolute links to where that media was Imported from. See this ARTICLE for more background.
Good luck, and if you have any questions, or something above was not clear, please ask, before you make the move, as the answers might save you some time, and extra work.