Ipad stopped working after 12 months

Have you tried to reset your iPad

Hold down the sleep and home keys for about 20 seconds. When you see the silver apple, let go and let it reboot. No data will be lost.

When you connect it to your computer does anything come up? If so you may want to just try a restore.

http://support.apple.com/kb/HT1414

You could try an Apple store if one is near you, however you are simply relying on the staff to take pity on you to get a replacement that is out of warranty.

You can also call back Apple to see if you get any other support staff or try escalating by asking for higher up members of staff - but this may just result in you waisting time & getting more frustrated.

Refurbished models are basically new devices based on the reports on here - Apple replace so much that the device should be reliable, clean etc.

It may be your best option.

If you are still dissatisfied you could look at your consumer rights, there is often protections in place for goods to be 'fit for purpose' and have a 'reasonable lifespan', this will vary per country and per region and you may want legal advice before beginning.

Another option you have is to look elsewhere for a repair, Apple don't repair these devices they simply offer replacements. Other companies will offer repairs.

There are many places online that sell parts too if you are willing & able to repair it yourself - obviously voiding the warranty and any chance of more support from Apple if you or anyone else opens the device. Diagnosing the issue is your biggest battle with that, combine that with how intricate the parts are & how it is put together you have more to lose than gain by opting to go that route.