Replying to Starting to look for a new computer

Hey guys,
So, graduation is coming up and I am off to college next year and I need a new laptop. I have had the same laptop for the past 6 years and it always needs to be plugged in, it can barely handle HD footage or Premiere. So now I am starting to look for a new computer to edit video and photo with.
I do not really know much about computers so I figured I'd ask you guys for your help.

Requirements:
- Needs to be a laptop due to the fact that I need to take it to college and travel with it
- Needs to be able to handle Premiere Pro, After Effects, as well as Photoshop
- Preferably under $800
- I do not really want a Mac

Got any suggestion? +k for help