G2 Possibly Needs New Motherboard Or?

Hi guys..

So I bought a LG G2 used on eBay. It was for 50 bucks or so and it was cheap because it didn't have a screen but the seller stated everything else works.

So heres what I did:
Purchased new screen x 2 (twice)
Both screens didn't work
Connected phone to TV through an HDMI adapter
The phone heats up while it's booting up sometimes

I can see the phone screen on the TV but the screen doesn't light up at all except it does have a tiny bit of backlight. As I touch the screen, it goes VERY slow, takes a second or two to respond.

How do I know if it needs a new motherboard or just new parts?
If it goes very slow but it shows on the TV, does that mean the motherboard is the issue?

Thanks in advance!!