I haven't had issues with a cage yet, thank goodness, but I have had to deal with other situations like this.
I would take pictures of how messed up it all is-the company may deal with lots of exaggeration and thinks it's just a bar or two bent up. Complain and be forceful, explain how you're paying a lot of money and expect a cage in new, functioning condition. The company you bought the cage from probably is thinking partial refund if it's still usable (like the bottom part is funtional and it's just a few bent wires on top-give $50 bucks back and maybe they'll stop complaining), or that you can return if it isnt functional and buy another. Try to ask if they can send a replacement and you'll send this one back? (and try to get them to cover all shipping too)
Let Midwest know how the other company is handling it as well- they don't want to get a bad rep with you because the middle man isn't handling customer service right, so they may work with you more-it seems like they'd rather the company dealt with it first.
i also would try to keep your chin in his old cage until you've got everything dealt with (and him and his stuff out of any pictures). The company may be fussy with you about how it was ok to have your pet in for a short time and wont like giving refund/replacements after that. Plus if parts really aren't fitting together right I'd worry about stability or it falling apart with my chin inside.
good luck, and maybe stock up on headache medicine in anticipation of dealing with them.
Whatever happens, the company shouldn't get away with selling a broken cage. If it's a shipping problem they should have means to deal with that. If it's a manufacturer issue, it should be replaced and the company can take the broken cage to Midwest and have it taken care of. If people are being really bullheaded I would even make a veiled threat about letting people know how horrible they were to deal with on here-if they know their reputation in a community is at risk they may help you out more.