My IPad Air will not turn on, normal steps to fix it do not work. What options do I have?

I have an Ipad Air that is a year and a few months old, it will not power on. It started turning off it's self, a few times I was able to bring it back by holding the 2 buttons at the same time for about 10 seconds but after a few times that failed to work. I have tried connecting it to the PC, the PC recognizes a device but does not bring over the device name or anything. I have tried doing a system reset from the PC but part way through it fails not being able to connect to the device. The warranty expired at one year, I took it to the Jump Plus store near me in Moncton, New Brunswick, Canada and they told me it is 'Power Dead' and that without warranty the only option they had was to do an exchange at the store but that would cost just a few dollars less than buying a new one through retail. I am wondering what other options I have. I understand it is not on warranty so I should have some financial responsibility in getting it fixed but I am very unhappy if the only option is to get it replaced at basically the cost of buying a new one. I have had several IPod's and Ipod Touches and all worked for several years with no problem. An electronic device that costs over 500 dollars should not fail after slightly more than a year with completely normal use, especially if there is not a cost effective way to repair it. Please let me know what options I have. Serial number is DMPLDPALFK10.