You may have read that this problem can be caused by a stuck shift key. Since you've been having problems with other keys, and everything is typing in caps, then I suspect this is your issue. The reason people say it's the shift key is because if you try and restart with the shift key pressed down, you will indeed come up with the safe boot page.
Then there's the part about it not accepting your password. Which, as usual, shows up as little dots in the password box. What you are not seeing is the fact that with your shift key stuck, you are typing your whole password in caps, which is why it's not accepting it.
If you are still under warranty, and can talk with the Apple people, at some point they may be able to get you to a page where they ask you to type in some text, but shoot - When you do, everything is in caps. This is the smoking gun, when it comes to the shift key problem.
One would think that these keyboards were more resilient, but in my case, it didn't take but the tiniest bit of moisture…just a mist of it…to mess up my keyboard. There are little dots of some kind of substance down in the chassis that turn color if exposed to moisture, and if they have turned, you are the one who will have to pay for the repair, even though Apple is likely to begin by telling you that it's all covered by your warrantee. If it is still in effect, that is.
If you are lucky there will just be some piece of debris under the key that is holding it down, but that was not the case for me. Figure around $300 or more for a keyboard replacement, or perhaps less through an independent repair person.