Well I have to say as far as repair costs go, around 60 dollars US isn't a bad cost. It is quite low on the repair cost end.
Unfortunately if it won't turn on at all, other than replacing the battery to see if that is the issue, or trying out a new charger to see if the other one was not functioning correctly, there isn't a lot you can do. At least not a lot that would not take a lot of work and more money than they want to charge.
Even if it is the display needing replacing, between the work to do it (which you would have to be very careful doing) plus the cost of the display itself, would be more.
Sounds like they are the best bet to me, unless your device is under warranty still. Then I would contact the manufacturer.