You can get any of the Nest Thermostats, it seems like they are
compatible with your system. Just remember to remove that jumper, it is
not necessary for Nest Thermostats.
Connect the thermostat to a computer. If the computer recognize this
device that means that it only needs a factory reset. If the computer is
not able to show the device then you can call to verify the warranty of
your thermostat and get a replacemen...