Not being able to login as
root (other than by using
sudo) is normal; Ubuntu doesn't set a password for
root by default.
/etc/sudoers means you can't use
sudo, of course. But creating a new group shouldn't affect
/etc/sudoers. You must have done something else.
The way to recover from this (short of reinstalling) is to boot into a single-user root shell. From there, you can fix
/etc/sudoers, and whatever else needs fixing. Be careful while you're doing this; it's very easy to break the system by manually editing system files like this and frankly you've already done so.
To get a single-user root shell, see this question. Quick summary: Hold down the left shift key while booting and follow the prompts to get a root shell.