Thanks for reaching out to us and sorry to hear about the phone. I'm sure you have gone through some troubleshooting with it but if you haven't tried any feel free to reach out to one of our live agents who can see if there is anything that can be done to get it working right again.
As for the switching over to the new phone, it all depends on which network you are on. If you are on the CDMA network you would need to order a new SIM card for the LG G5 but if you are on the GSM network you would not. GSM SIM cards save your phone number on the SIM card itself while on CDMA the phone number is saved to the device itself.
If you're not sure which network you are using with Ting it will tell you in the Device Settings section of your Ting My Account or feel free to reach out to us by phone, online chat or email and we would be happy to take a look for you.