Something is very wrong w/ my computer, please help?

Ok, I'm not quite sure how to concisely describe the problem since it's made up of so many things which have effectively rendered my computer useless. I think it's a virus, but my virus scan didn't come up with anything helpful, so.

Last night I was watching Youtube videos and editing some photos when I noticed I had to tap at the touchpad several times before the computer responded. Then it stopped working completely (ie I could still move the mouse pointer but couldn't click using the touchpad). I switched windows to look for a solution on the internet, but when I clicked at the address bar of Google Chrome the cursor started moving ahead on its own, like someone was pressing the space bar - but I wasn't. This made typing impossible as there were huge gaps between each letter. I switched the computer off and switched on again (thank you, ICT lessons), but the problem hasn't disappeared - only now, the mouse pointer occasionally disappeared when stationary. It was getting late so I switched it off again and went to sleep.

This morning as I was starting it up it was making bleeping noises it usually makes when I plug it in/unplug it from power. I tried to type in my user account password... and couldn't. The capslock wasn't on, I sure didn't forget the password overnight, but I kept getting error messages and couldn't log on. Worse, when I tried to switch to an account that wasn't password protected, it kept jumping back to mine after maybe 3 seconds. I finally managed to click on the icon of the second account and logged on.

The touchpad still doesn't click, when I opened Chrome and clicked on the address bar it reacted like I've clicked with the right handside button (so I couldn't type) and the mouse pointer still randomly disappears. I ran a quick Norton scan and it came up with 22 "risks" which it apparently "fixed" but the problem still hasn't disappeared. I would be v. v. grateful for a prompt reply as the laptop isn't actually mine, but my father's (who keeps the bulk of his treasured photographs on the hard drive).

EDIT: I opened it in Safe Mode. the touchpad now works, but random keys on the keyboard have stopped working. Others come up with random combinations when I press them, eg. "tu" instead of "t", "p-]" when I press "-". I can't even reinstall keyboard drivers, because I can't type in my administrator's password.

Have tried using a different keyboard? That is probably the first thing I would do, or if it's a wireless keyboard/mouse combination put in new batteries.

It's a laptop!! So I'll probably use a second keyboard to reinstall the drivers for my original one, but there's obviously more going on that the drivers won't fix.

It sounds like the actual keyboard has an issue, not software related. When you said it makes beeping noises when turning it on, it's almost the same as having a stuck key. Depending on the model of laptop you have, I would pull the keyboard out, plug in a USB keyboard and test to see if you get same results. There are several guides out there taking the keyboard off, usually it's a couple screws.