They'd probably just tell you to complain at the ticket office (if it's still open they might be able to verify your credit card?) or phone next day.
In theory it should be simple to identify who you are in conflict with if the ticket is not general admission. They would just have to send an usher to the seat. However, it is difficult to determine who defrauded who without a whole lot of investigation.
You would have to establish the entire chain of custody for both of the tickets. Three possibilities with different culprits are: the original purchaser double sold the tickets, a third-party got the barcode and sold a fraudulent ticket to whoever is in your seat, or the person in your seat made the fraudulent ticket themselves.
neither the ticketmaster folks nor the venue folks tend to be super compassionate in my experience. it's a real mess though, the venues often have no in-and-out privileges (possibly due to how scanning invalidates some 24-hour key), so even as a law-abiding consumer, you're stuck at an event for the whole time just to deal with ticketmaster's implementation details.
i'm sure others have said this, but that is definitely a business that wants disrupting. there's so many bits of tech that could make this experience better and safer for consumers, but i suspect ticket fees are more profitable than user experience.
As an aside, many festivals and venues don't disallow re-entry due to TM implementation (I've been to enough TM ticketed events that have re-entry). They ban in-and-out so that you cannot go elsewhere to drink or eat without the festival surcharge and kickback.
Generally, as far as I've seen, you'd be SOOL. (Shit out of luck, is that an acronym yet?)