Going to wager that you've defined a place for Flash to find the classes necessary for this platform game. That said, the file path will have changed when moving to any new computer, PC (unless somehow the user name is identical) and definitely Mac.
Simply try going into publish settings for ActionScript and make sure that any folders you have specified to find your class files are valid. Let me be clear on this. Even RELATIVE paths will be incorrect. The best thing to do is always hit browse and just manually find the location of the class files, and hit ok, for every path you have.
If you're doing import statements, be absolutely sure the files are available relative to the FLA.
From the errors it just looks like it can't find the classes it expects, or you moved them and didn't tell Flash where to find them. Flash has always required me to repoint my included paths uncountable times and even re-link any SWCs and runtime shared libraries. So relink it allllll, so you're absolutely sure Flash can find the code.
Thank you so much! Your explanation was complete enough for me to understand what you meant. I found that somehow the folders game, animation, and tools had gone missing from my project folder. How, I don't know. Anyway, I found them in older backups and simply placed them in the right folder (without reassigning paths, yet). Now my game publishes without a glitch. However, now there are some weird animation glitches - my character no longer turns around to run in opposite directions when I press A or W. But that's another discussion.
Glad you hunted down the first issue! The second one sounds like a great learning experience. You're welcome and good luck!