iPhone 4s is not turning on

Hi,

My iPhone 4s(First device🙂) was dead now and not turning on😢 though the battery was charged fully.

Yesterday, I tried and tired by holding the power and home buttons at a time, and suddenly it turned on.In a couple of seconds again it got dead.

I connected using itunes and it is detecting and asked me to restore the firmware and i accepted it. Even after the restore, still not turning on.

Please suggest me some inputs . I am afraid to go service center as there is no warranty covered now and am not sure what will be the charges.

I am in Doha, Qatar now and suggest me the service availability in lower prices.

Thanks

Santhosh