I Don't Know What Is Wrong With My Laptop

Hi, I just really need some advice. I keep having issues with my laptop, and I'm at a loss for what the problem is. I don't know if I may have a computer virus, I've been hacked, or if it's a problem in some other way just with the computer.

Operating System: Windows 7
System Manufacturer: Dell
System Model: Inspiron M5040

What's Wrong:
1.) My mouse has a mind of its own. It won't click things by itself, but it keeps randomly moving on its own. It's very annoying, because it makes it difficult to click on what I actually want it to click on. Plus you know how if you pinch your fingers on the track pad it'll zoom in and out? It constantly will do this, which makes it even harder to operate. Sometimes it will go back to the previous pages when I'm really trying to work on something important. I've frequently cleaned the track pad very well.

2.) It'll automatically type the most random things. Like "-==--=", it's always up there in that area of the keyboard, and pretty much just dashes and equal signs.

3.) It'll just randomly crash sometimes. Especially after #2 happens. It'll then start back up once I hit the on button again, and asks me if I want to run in safe more or start regularly. Also, sometimes before it crashes, if I am using Chrome, another tab may open by itself and go to the Chrome Help page.

I feel like maybe I have a bad virus or something because I've read these could be signs of that, but for the life of my computer, I've had Norton Security System and I've ran probably hundreds of hours of scans. However, my yearly subscription just ran out, so I've switched to AVG in the last week. There was never a point where I was without protection.

Additional Info: Before my Norton had expired, I downloaded AVG and ran a free scan. The first scan that was ran, a Trojan Horse was discovered. No other things have been found since. I don't know where to further check if there's problems other than running the scans. If you think it is a virus/ hack please give me advice on how to get rid of it?

Thank you so much for your time in reading this, and for any thoughts you may have of what the problem could be!