Are you at fault in a car accident if the other person cut in front of you causing the collision but you were ticketed for having an open container of beer?

The open container is definitely a big issue, particularly if you were tested at the accident scene for being under the influence and you approached or surpassed the legal limits. If you weren't tested, or if the test showed that you were within the legal limits, the open container shouldn't have much bearing on the liability investigation -- in theory. In reality, it will probably cause a few raised eyebrows, particularly if it's against the law to drive with an open container.

As for the accident itself, you don't mention if it was a straight-on rear-end impact, or fender to quarter panel, etc. If the other vehicle cut in front of you, slammed on his/her brakes, and you rear-ended him/her, the burden of proof essentially falls to you to prove that you're not liable (normally, the burden of proof falls to the "injured" party, but in a rear-end accident, it's assumed that the rear vehicle is at-fault).

How would you prove the front vehicle is at-fault? Almost always, you'd need a witness, since the front driver will rarely own up to his/her wrongdoing.

A scene investigation showing your tires' skid marks might be helpful, though not conclusive.

Now, if this is simply a case of the other driver changing lanes and striking your vehicle, you have a much better chance at proving liability against the other driver, particularly if that person admits that he/she was, in fact, changing lanes. Of course, this is where your open container comes in, because a claims adjuster might argue that by drinking, you were not able to keep a proper lookout for the other vehicle, or were unable to react defensively. You could be assessed a hefty bit of the negligence for that reason.

Good luck!