Which new laptop (current broken)

[BarackObanter]

I have a 2014 HP Pavilion that I got for Christmas 2014. Before you laugh, I had no idea what was a good laptop, and what was bad.
Yesterday night, I leaned on my laptop after plugging in my phone to charge, and the top left of the screen is now broken, and the touch function does not work on the left side.
My question is, then, what laptop should I get? I would like something with 4 physical cores, and under 15 inches big. I like portability, though I won't be moving it around much.
Attached is my current laptop's specifications. A dedicated gpu would also be helpful
http/prntscr.com/cdyavw

Update 1: now the cracks stretch the entire screen

 

[bobmanuk]

what is your budget? and general location? do you have a specific requirement or use?

I live in Malta and highly recommend the Lenovo Ideapad 100, is a 15.6in screen, has a geforce 920m, 4gb ram and 1tb hard drive and costs €400 obviously its not going to be easy for you to get but you could check your local computer shops or classifieds. I have used Gumtree (UK) previously and gotten some very good deals on computers that arent very old.

 

[BarackObanter]

England, UK is my location, and I'd say my budget is €1000 or £800.
I would appreciate 8gb RAM and a discrete graphics card

 

[hang-the-9]

England, UK is my location, and I'd say my budget is €1000 or £800.
I would appreciate 8gb RAM and a discrete graphics card

For that much you should be able to get a system with a 960m video card. Really just about anything with that video chip will be good, just see what's available in your area, models are different in each area.

 

[velo3100]

Whats your usage?