It boots and POSTs fine... until I connect a hard drive to the power supply, at which point the PC will switch on for 1-5 seconds and then switch itself off. I've tried 5 different drives, both ATA and SATA, and it won't work with any of them... although it will work with a DVD drive connected.
It's also being a bit temperamental with a Radeon HD5450 graphics card; sometimes it won't stay switched on until I've removed that as well.
The only component that's not brand new is the power supply, which is a 450W model with 20-pin and 4-pin connectors. The motherboard's manual recommends using one with 24-pin and 4-pin connectors. Does it sound as though I need to replace the power supply, or is there something else going on? There are no beep codes at any point.
If you go to Best Buy, avoid their Dynex and Huntkey/Rocketfish PSU-shaped objects. Many of the latter burned during testing at HardwareSecrets, and the former received a particularly scathing review over at HardOCP. Fortunately, you should be able to find Antec and/or Corsair there. They'll make you pay through the nose, but a cheap PSU is never a good choice.