We cannot forget the Portable installation, because I think that's exactly where you went wrong, and is the fundamental thing you don't get. The behavior you're experiencing isn't normal for a regular install, from what I can tell.
You can only make portable installs using a machine that has a regularly installed, licensed, copy of MC installed.If you installed the copy of MC on the second machine in Portable mode, then you need to uninstall it completely, and start over on that computer. You can't install in portable mode "on" a computer that doesn't already have a copy of MC installed. I really think that's the cause of your trouble. You were up to some funny business with the portable installation (not being nefarious, just confused). Portable installs are for installing MC onto a USB stick, or something similar, and (again) can only be
done using a computer that
already has a licensed copy of MC installed and working "in normal mode".
Otherwise, assuming you fix that, or don't have that issue... You can add a license for MC in one of two main ways:
1. You can enter your Registration Code (this is the code you get when you bought MC) directly into the application. You can do this from the splash dialog that comes up in Demo mode on launch, or you can find it under the Help menu once MC is running. This adds a license for that install automatically. It should pop up a web page and give you a "license installed" dialog message. You don't have to do anything (though, if you need it for a different PC, you can download the installation key file from that web page). Licensing it this way counts as a "restore". You get 10 restores per rolling calendar year. If you screw up somehow, though, and use them all up, ask for help and they can be reset if needed.
2. When you do #1, they email you an installation key (or you can download it from the web page that pops up). This is a MJR file that you can double click on any
other machines to install the license (the one where you did #1 gets the license automatically and doesn't need the installation key file). These last for 14 days and can be used on any other machines that you own. To use one of these, just copy it to any computer that has an unlicensed copy of MC installed, and double-click the file. This will launch MC, and install the license. MC does NOT ask you to do anything with it. It typically just will pop up a dialog box that says it was installed. If the MJR file is no longer valid, then you'll get an error and need to generate a new one (or just enter your Registration Code into the program, which is the same thing).
Option #2 can also be used to add a license to any computers that can't get online. You can generate an installation key manually by visiting this page:
https://rover.jriver.com/cgi-bin/restore.cgiAnd then use the MJR file to install the license. There is no benefit to #2 other than that it doesn't use up a "Restore" to license multiple machines (so you can save them a bit more if you have two or three computers). But, if needed or your MJR file expired before you got to it, just use #1.
If it isn't working the way described above, then the most common culprits are anti-virus programs doing something weird, or having run registry cleaners of some kind which broke your installation of MC. The simplest solution to the latter is to reinstall MC. For the former, your anti-virus program shouldn't be interfering with an application like this (though it has been known to happen) and you'll need to disable it or uninstall it or fix it somehow to proceed.