The pump is on the passenger side of the engine just below the exhaust manifold. It is on the front of the engine and is driven by the poly/multi belt.

It has a U shaped hose that points down and is open (air intake?) and another hose with a valve/thermostat on the back of it.

I think it's the air injection pump.

The car wouldn't start and I kept cranking it. It eventually did start and promptly started smoking under the hood. Switched it off, popped the hood and observed a smoking belt/pulley combo on said pump. The pulley was tilted to one side. Not sure if it was the belt (which is 5000 miles old) that was smoking or the pump or both.

Would it make sense that the car wouldn't start if the pump was failing? Or perhaps it was putting enough resistance on the belt to mess things up?

Your suggestions and advice are my happiness. Particularly along the DIY angle.

Thank you!

EDIT: I'm almost certain it's the air pump. A remanufactured one is about $200 on ebay. Has anyone here replaced one before? How much stuff has to be moved to get to it?