I downloaded the new Beta for Mac and now it says my username/password is invalid. I've already changed my password and got it recovered but it says the same thing. Any suggestions?

As far as I know, the beta is can only access the PBE (Public Beta Environment) and not the live servers at the moment. They are still testing the mac client on the Beta servers before releasing it to live. Therefore, unless you have a PBE account, you can't use Riot's Mac client atm. (PBE is only open to registration for a while every several months.)

Boompje has a mac client that you can download here, but it has bugs and doesn't work for some people (click the wrenchbox link, the mediafire link got shut down).
http://www.boompje.net/download/ilol

Thank you for that information and how long will it take to release full version of LOL for the mac. Sorry if I'm being inpatient.

To my knowledge there haven't been any updates wrt a time frame. It'll be out when it doesn't break things, and trying to predict it further in advance will more often than not result in people being upset either because the date is 'too far out' or if it has to get pushed back.

And the wait is over, apparently. The Mac client is now in open beta.