Hi, to determine whether the problem is the monitor or the motherboard/gpu, connect an external monitor to your laptop. If external monitor works with no problem, your laptop monitor is at fault. If external monitor doesn't work, you have a motherboard/gpu problem.
As far as where to send it to get fixed, if your laptop is still on warranty, contact acer for technical support. If it's out of warranty, find a local repair shop.
As for the prices, a laptop screen problem is a relatively cheap repair, unless the LCD panel has been discontinued and there's limited supplies of it available. Motherboard/gpu issues are much more costly since in most cases the solution requires full replacement of the motherboard with all the components.