Basically, I need help getting a laptop to match all, if not most, of my criteria. WIth my criteria being..

CRITERIA:

Price: Max $650 (the less the best)

Screen: 14'' Matte screen (I hate glossy/mirror finish screens), 1366x768p - 1920x1080p (Doesn't really matter as it is a school laptop, but the bigger resolution the better)

Battery: Minimum 2 hours under load (4 - 10 hours of normal use)

Weight: 1kgs to max 2.4kgs (the less the best)

Performance: Powerful enough to run light-weight games (such as Rocket League and League of Legends). I'm guessing this would require a dedicated GPU but I might be wrong.

Keyboard: Backlit (not required, but good to have), Type-able (I'm a student).

OS: Windows 10

RAM: 8GB (could maybe go down to 4GB if the other Criteria is filled out)

Storage: Doesn't really matter. Prefer SSD, but I won't really bother.

Ports: Minimum of 2 USB (2.0, 3.0, 3.1), 3.5mm Headphone jack and an HDMI. An SD Card reader would also be practical, but not necessary.

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I might be asking for too much here, and I probably am, but something like this would be my "perfect" laptop. If you manage to find anything, please do let me know. I have found one myself, but I'm not sure whether its powerful enough to run the games I have listed.

Any feedback would be appreciated.
Thank you in advance.