If you are worried that it's hardware, run the apple hardware test. (I honestly don't know what would cause the snow effect, but I'd definitely be thinking hardware).
Insert OS X disc 1, turn the mac off then back on and hold down the D key. Choose language for the test and run the test. If everything is checks out, then it's very likely a software issue.
If you have Disk warrior or Drive Genius, you might be able to repair the drive errors that disk utility won't.