How to repair my mobile?

I have a Nokia 3110 (the original one). It was bought in August 1997 (if that helps). It's Black and looks good apart from a scratch on the Antenna.
I have kept it for all these years (my first and only phone) and was ok untill two days ago. It lights up when I press any button but it switches itself off within a few minutes (I am sure I have NOT turned it off) Its not the battery that is the problem as I have tried it with 5 different batterries and it does the same thing. Is there a faulty connection inside? The signal is good and I can make calls but when it cuts off I'm disrupted from these calls. It gives no warning. One minute perfectly fine the next minute off. Even when the battery is full.

I'd be gratefull if u all could help, even if its just suggestions and not facts. I really like this phone...CAN'T LIVE WITHOUT IT.