My iPhone only works on charge?

I have an iPhone4s. A couple of months ago it kept restarting so I rang my network provider (Orange) and they sent me to a shop who replaced the battery for me. It worked fine for about three months and then today, the screen just went black. I put it on charge and it will turn on but then reboot over and over and over. As soon as I take it off charge, screen goes blank and it won't turn on. Orange refuse to fix it. Apple won't fix it as it's out of warranty. So unless I figure out what's wrong with it, I'm faced with a £500 bill for a new phone.

First of all scan your device for viruses if it is clean then your battery is a goner
Just replace it!

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