Hello again, I apologize deeply. You said 'no cooling' I *assumed that you had cooling along with the furnace, and that it was simply not working.....and in that case there would be a unit that sits outside that runs in the summer.
That said, the issue of a W2 terminal remains... that is the *second stage* heat function. Your old NEST thermostat had second stage capability, the new thermostat you bought does *not have second stage capability.
In other words it is the wrong thermostat for your system.
Any 'conventional two stage heat ,24 volt thermostat that includes the following terminals, R, G, W1, W2, and C will work' if you get one that one *does not say 'heat pump' anywhere on the box, it will also be easier to wire and program. If it says 'heat pump' on the box, along with the words 'conventional system' and includes and O/B terminal or terminals then it will be more difficult to wire
Such a thermostat will generally also have a 'Y' terminal, that is for cooling, if you do not have cooling then simply do not connect it.
Again I apologize, on this end I am 100% totally blind to what you have, so I ask questions to narrow that down. There are literally thousands of different configurations the market... first step is always to determine which of that range of options that you have.
If you want to buy the thermostat locally, take this note to one of the more experienced clerks in a large hardware store that sells thermostats, then have them select a 'conventional 24volt thermostat with two stage heat' (that is not also for heat pump).
If you are going to buy it on line, just say so, and I will located one for you.