Umm -- being thick here, sorry: everyone's assuming that the phone will not work when plugged into its charger. Is that so?
I mean: I recently changed my phone for the same reasons: my phone worked ok when plugged in, so I transferred all data (not much!) to the SIM, then swopped the SIM out to the new phone, transferred all data to that phone, then swopped the new SIM back in. (Advice to do this is in my new phone's instructions booklet.)
...But I guess your phone's not working when plugged in...
John