My camera is frozen, won't turn off or on Canon Ixus 75

Simon Hurst, the Ixus 75 was sold as the PowerShot SD750 for the North American market. Anyhow, check the battery door and make sure that it still makes good contact. Also, check the battery contacts inside the battery compartment, make sure that there is no corrosion or foreign debris. You can clean those with high grade of isopropyl alcohol and a cotton swab. I would also suggest to check the battery itself with a voltmeter to see if it indeed shows the appropriate voltage. If that does not work, it may be time to disassemble the camera, using these guides and to take a closer look.