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Hi VX1, welcome to the community!
If you have tried different chargers and they haven't worked then it does seem like a hardware issue. However it might be worth trying to run a software repair on the handset to see if that helps, if you would like to give it a go just download PC Companion. Once installed, to back up your data first press Start under Backup & Restore and follow the on-screen instructions. Once the back up is complete, press Start under Support Zone > phone/tablet software update > repair my phone/tablet > continue > accept data removal > next > wait for prepare > select phone > follow connection steps.
If this doesn't work then contact your local Sony Xperia Customer Care team, so your handset can be assessed for you.