How do I move and old version (V3.0.2) of Premiere Elements to a new computer?

I was able to install it, but haven't been able to get it to run with full functionality on Windows 7.  I expect that Windows 10 won't be any better.

Unless you are installing it on Windows XP, you really should buy a newer version.

Deactivate it on the old computer and then install it on the new.

That's assuming you still have the installation discs.

Older versions of Premiere Elements are available online. However, they don't go back ten years.

Download Adobe Premiere Elements 15, 14, 13, 12, 11, 10

There also may be components in version 3 (including the 3.02 update) that no longer activate. It really might be worth considering upgrading or buying a more recent version of the program.