If you take your computer to the Genius Bar at Apple, they'll boot it from an external drive and take a quick look at things to try and determine what's wrong.
The most likely scenario is either a damaged operating system, a failed hard drive, or a defective optical drive flex cable.
Try leaving it on for 10 minutes or so. Does a flashing question mark eventually appear? If you see a flashing question mark, but it takes a minute or more to appear, it's almost certainly a failed hard drive or a defective flex cable.
(tech note: if a device on the ATA chain fails to respond to the computer's signals, the system may hang at a blank white screen for several seconds to several minutes while the system waits for a response. the optical drive flex cables on some glass imacs are defective, resulting in this "blank white screen" symptom)