I have used several MAMP installations so I may be able to help you figure this out, but I need to know some details.
Also, before we begin, I noticed you moved everything into your htdocs folder on MAMP. Just so you know, you don't have to do it this way... you could leave them in your sites folder... then just go into MAMP "preferences", select the "Apache" tab and change the document root to /Users/logicwest/Sites.
Then when you set up your testing server in Dreamweaver, you would just denote the test URL as siteFolder/ and you would be good to go (of course this is also after selecting the ports tab and clicking "set to default Apache and MySQL ports which will make your port 80 for Apache and 3306 for MySQL).
So getting back to your problem... when you fire up MAMP, does MySQL not start at all... meaning the light remains red on the MAMP interface? If you are getting a green light for both Apache and MySQL, then everything is starting fine. Then we know the problem is with the GUI and not the server. If mySQL does not start in MAMP it could mean a number of things which I will make suggestion once I hear back.