You have a bad battery. This does happen. It is not always the battery cell itself, there is a electronic circuit in the battery that can shut it off and not allow it to charge.Blinking orange is a feature of the 6D charger that tells you, depending on how many blinks per second, how much/little the battery is charged. (See the manual for details.) I found it annoying at first, but now I kind of like it. It can sometimes take a long time to charge a 6D battery. Still, if it goes much beyond the time stated in the manual, call Canon. Also, I just checked my 6D and it powers up just fine without a card. It even tells you it has no card.
I had found out about this (pretty cool) feature. It was blinking at I guess 3x/s. I charged it for a really long time (a day) and then again (after trying it out for the first time) over last night. The camera doesn't even start The charger keeps blinking. I guess I'll just call Canon tomorrow, maybe they can help me out quickly.
Thanks again guys, this is an AMAZING forum, the only problem is seeing such fantastic pictures posted and realizing how much I have to learn!
Unfortunately, you may need to exchange the entire camera, that's what others have had to do. Its probably your safest option, in any event.
If Mt. Spokane is right and it's the battery, you could always find a local store and buy a battery. This would give you the ability find out if it really is the battery and, since you were wanting to shoot this weekend, you could enjoy the camera then deal with Amazon on Tuesday. You'll want a 2nd battery anyway, so that would not be a waste of money.