I've uploaded the files, verified permissions and set up the database. When I run the install, I see the monkey, and I enter in my details. It appears to go well, until a screen showing only: "Oops"
Using Ben Croker's Craft Requirements Checker, I get:
Minimum requirements met. Craft can run on this server!!
The server is running MySQL 5.1.56 with InnoDB, so I believe it's capable of running Craft.