Thanks for your help guys. I got the system to work.
The seacock to the pump inlet was inexplicably partially closed for whatever reason, so I opened that up. But that wasn't enough.
I had to clean out the strainer that was gunked up. Again, not enough to get it going.
Finally, I had to burp the system by unscrewing the strainer for a couple seconds while the water was flowing. This did the trick.
Now the cabin feels like what an airconditioned car would feel like in the Texas heat. It's definitely going to make the summer out at the lake more bearable for the family. I'm actually quite surprised at how efficient at cooling the system is, given how small it is.