Sorry to resurrect an old thread, but I thought I would share the solution that I found for my problem.
Unfortunately, the PX4 firmware stack will not compile without cloning from Git. The first line of code in the Makefile checks whether or not the code was sourced from Git and throws an error if it was not.
As I stated in my original post, I had tried copying the entire Firmware directory onto a flash drive or a network drive and then transferring that to my new computer, including the build directory. I'm not sure why, but for some reason that approach did not work. I don't really know enough about the copying process to say why this did not work; I can only say that it didn't.
However, I was able to get the code to compile by using SFTP to transfer each sub-directory one by one into a Firmware directory that I created on my new machine. I copied all of the subdirectories of Firmware EXCEPT "build" using
get -r <folder name>. It is important to copy the ".git" folder(s) as well. I used
get -r .git* to copy over all of the Git files.
After copying everything over in this manner, the code compiles fine. I hope this helps others that may have run into a similar problem.