Latitude E6400 screen with black triangles on bottom

Hi there,

 I have an Latitude E6400 that I am using for medical school. It recently started to have a lot of issues right when my warranty ran out. Our school charged us around $2000 for this laptop so I'm definitely unwilling to just throw it out yet. 

so it first started that when the computer goes to sleep, the screen would go white instead of black. Then it started to have these little dark triangles all along the bottom of the screen (ive included a picture below). And now, when I use a separate monitor via a monitor cord, the 2nd monitor is fuzzy and changing the refresh rate doesn't fix it like it used too. my classmate who has the same laptop does not have this issue when we connect his laptop to the same monitor. in addition, sometimes the screen will just be dim and I wont be able to see anything (well faintly). 

interestingly, when i connect my laptop to my television using HDMI cable, the screen is perfect with no issues?!? Does any of this narrow down what the issue could be?

My question is, what's part is not working and is it an easy fix or is it time to toss this laptop out? Any help will be greatly appreciated! Thanks guys! We use these laptops to take our shelf exams and so I'm terrified that in the middle of my exam the screen will go out.