Usually it means your new thermostat is not compatable with your old system.
It is possible one relay or two relays must be added for for proper operation OR it will not work what so ever on your old system. This is why they have professionals that deal with these problems.
It would be easier to do a better job shopping next time so you get the correct thermostat to start with. But here again a professional would have never purchaced a thermostat that would not work on your old system.
Life is a learning experience.
BTW what is the EXACT complete model number of your old thermostat. I will see if there is a conversion.
http://customer.honeywell.com/techli.../69-1900EF.pdf