We could not activate Mass Effect 3 on this computer

A new EA account, refunding, and rebuying aren't necessary for this error. This error only happens for a couple of reasons. The main ones are

You owned it through EA Play and that became inactive
You haven't played so the license file is just corrupted
Another user downloaded and logged in and now you are trying to play
The game and the platform are on different drives

It's typically a pretty easy fix if the account you log into owns it. Below are the steps we take to resolve those errors. The main calls are the license files and registry files. It seems like a lot, but they are pretty easy steps.

Delete EA License Files:

• Make sure the EA app is closed.
• Press the Windows key and "R" at the same time.
• Type or copy and paste "%ProgramData%\Electronic Arts\EA Services" (without the quotes) into the new Window > ENTER.
• Enable View Hidden Files and Folders
• Delete all files in the "License" folder.

Please clear your temp files:

• Press the Windows key and "R" at the same time
• Into the new window, type or copy & paste: "%temp%" (Without the quotes.) > hit "ENTER".
• Your Windows Explorer should have brought you to the "C:\Users\>your user name<\AppData\Local\Temp" folder. > Delete all files and folders in it.
• (If some files or folders can't be deleted, reboot and try again.)

Additional steps:

• Go here and download "Revo Uninstaller". (The freeware version and portable version work too.)
• Run "Revo Uninstaller" > Uninstall DAI.
• Revo will ask you which cleaning method you want to use at the end of the main uninstall. > Select "Moderate" > Browse
• If "Remaining registration content found" is displayed > Select All > Delete > Next
• When "Remaining Data and Folders" is displayed > Select All > Delete
• Run "Revo Uninstaller" > Uninstall EA Desktop.
• At the end of the main uninstall, Revo will ask you which cleaning method you want to use. > Select "Moderate" > Browse.
• If "Remaining registration content found" is displayed > Select All > Delete > Next
• When "Remaining Data and Folders" is displayed, Select All (Making sure the "Origin Games" folder is not in the list) and delete.
• Restart the PC > Reinstall the newest version of the EA app.
• Reinstall the game > Test.