After leaving on small overhead light, vehicle won't start with a boost and turn on the remote and horn starts blowing.

How are you boosting the vehicle? Sometimes a weak booster can't overcome a completely dead battery. Plenty of other possibilities.

If using another car for the boost, first make sure the boosting car is running, then put the cables on both and make sure you have a good connection. You should actually hear a momentary change in the idle of the boosting car when you get a good solid connection. Make sure everything in the dead car is turned off, then allow about 1 or 2 minutes for the boost car to charge up the dead car before attempting to start it. If you are using a portable booster make sure that is fully charged before using it. If either method doesn't start your car the problem is more than just having left a light on. With all the electronics in cars today the parasitic draw on batteries has increased greatly. Some cars have systems that allow them to go into "sleep mode" like computers do, to avoid this problem somewhat. Being what the systems are today, with your battery probably being the original to the car it is 7 years old and that is really pushing your luck. Batteries do eventually break down inside over time and will or can short out, so if you can't jump start it best bet would be battery is too far gone so just replace it and you should be on your way.