Bad login means nothing than that the account you are(n't) using is not legit. Therefore, it won't allow you to connect to servers.

Online-mode

Server checks connecting players against minecraft's account database. Only set this to false if your server is not connected to the Internet. Hackers with fake accounts can connect if this is set to false! If minecraft.net is down or inaccessible, no players will be able to connect if this is set to true.
Turning it off is asking for trouble.



And yes, your mods will also cause problems. But the first thing it does when you connect, is seeing if your account is legit. As yours is not, it won't even check if your version is the same as the server's (including mods).

Lastly, the earlier you buy it, the cheaper it is.
The alpha costed only €10, the beta €15, and the final will cost €20.
Also, people who have the alpha have a license for ALL future versions. Including those on other platforms (confirmed by Notch, the developer).

The beta accounts have signed up to whole different terms. What exactly, I can't recall, to be honest. But regardless, buying is the only solution if you want to play it with us.

Why are you deciding to wait anyway? When having a legit account, you at least stay up-to-date all the time.
It just saves a lot of hassle... and it costs only €15.