Sorry, but drops to computers are always a bad thing. A 'minor drop' could crack any number of parts, dislodge a connector or cable, cause something to short out, and damage the hard drive. You could have just damaged the power connector in the laptop or destroyed the entire motherboard and possibly the hard drive and other components and it's hard to say without looking at it.
As for pricing a repair, that's going to vary significantly by your location, the shops available in your area, the cost of any replacement parts if required, and how much the service charges for labor. It could be $50 or could be a $1000. You best bet is to contact an ASUS repair center and take/send it to them: https://www.asus.com/us/support/Service-Center/USA Your alternative is to take it a local shop and see what they say; they might be cheaper especially for a simple jack repair or loose component but they may have trouble sourcing parts for a more significant repair.
As for pricing a repair, that's going to vary significantly by your location, the shops available in your area, the cost of any replacement parts if required, and how much the service charges for labor. It could be $50 or could be a $1000. You best bet is to contact an ASUS repair center and take/send it to them: https://www.asus.com/us/support/Service-Center/USA Your alternative is to take it a local shop and see what they say; they might be cheaper especially for a simple jack repair or loose component but they may have trouble sourcing parts for a more significant repair.