It is possible that the PRAM battery is week, or the OS corrupted the monitor settings. I had a similar situation yesterday with Tiger, whatever the cause.
If you clock needs to be reset after a shutdown overnight, you need a battery. Radio Shack has them, although they don't always know they do. Also you can buy them online for half the price, about $7.
Reset the PRAM. As you reboot, hold Command (the Apple key) Option P, and R. It's a Vulcan Death Grip. (Old reference. Sorry.) Hold all four keys until you hear a second BONG sound, then let go. That resets some basic settings in the Mac's non-volitile memory, where it keeps such info as what disk to use for booting, the monitor resolution, and other data it needs before the OS is loaded. (In some cases it is neccesary to hold it down until it bongs five times. I don't know why, but I read it somewhere a long time ago.)
If you ever see anything on the monitor, it is probably OK.
Another test would be to isolate the problem. Hook the monitor to another computer, and the computer to another monitor. You may need a friend or a friendly computer store for that, but it is a sure way to find out which one is the problem. Look in the phone book for used computers. You can get a monitor to test with for $10 sometimes.
