Uhm no I think your WAY overvaluing it for a number of reasons. One it is used, so that cuts whatever value you think in half (the next owner has to take it without warranty, as is, and with no guarantees other than its 'works'; so with that much risk would YOU honestly pay for someones second hand computer then buy a new one?). Second you have broken key parts, so that means they need to pay for it out of pocket (or you going to fix it before selling?) so the costs to have a professional, plus the same parts (customized container for the drive, per model and manufacturer makes it expensive) would again reduce it by that value. Basically your looking at maybe $100-200 at the absolute most as someone could use it 'for parts' with another same exact model and get one working PC out of it to resell / hand off to their kid.
That said, if you want a Gaming Laptop, you have to pay serious money, because your taking higher performance level hardware (then what Grandma would us) to fit in a portable system and power by battery without only staying 'alive' for 15 min or so, and not weight 12-15Lbs (which they used to).
To pay for that will be around normally $2000USD. The top tier is i7, the next lower is i5 (like you have) or AMD Highest end CPUs (8xxx series). You would want a drive with 7200RPM, or better yet dual SSD and HDD so you get nearly INSTANT on and very very very low 'load times' of maps and such. Lastly you would want a separate video card not a Integrated Graphics only solution, on NVidia side minimum of a 670M to the 7xx series, on the AMD R7/R9, or if necessary a AMD 7xxx, but that is risky as those are hitting their 'end of life' now as well.