Mouse and Keyboard odd behavior

I have the white IMac with the 2.16 processor. Recently the keyboard and mouse have been acting up, where they just become unresponsive. Typically it happens when you try to wake up the mac after it goes to sleep. When you hit a random key on the keyboard, it wakes up and brings you to the log in box. From there nothing happens. It won't allow you to type anything in either the ID or PW field. Can't click on anything with the mouse either. The odd thing is that it will let you select the shut down option from that log in box, and it will let you type in the user name and PW to shut it down. But if you cancel out of that and try to go back to the log in screen, it goes back to being completely unresponsive. If you shut it down and restart, usually it will work, although sometimes you have to do it a second time.

It get a little weirder. I have separate accounts for myself, my wife and my son. My son and I can pretty much work normally once we get past the prior issue. But my wife is unable to do anything. She can log in okay, but then it won't do anything. It won't respond to any input from the mouse, and the keyboard is generally useless.

I have the apple wireless keyboard and mouse. I have tried using a wired mouse and keyboard from my PC, and the results are exactly the same. I have not made any hardware changes; i did replace .5 GB memory with a 2 GB memory about 6 months ago. This problem started about a month ago.

Also, not sure if this is related, but sometimes, the display has a line running through it, not always in the same place, where the picture does not display properly.

I have run repair permissions on several occasions, but nothing has changed.
Any assistance would be greatly appreciated. Thinking about replacing the HD, but that seems a bit drastic at this point.

It sounds like a hardware problem although you could also have some corruption throughout the user accounts.

Run the Apple Hardware Test from your original DVD set and let's see if it comes up with anything.