Start from the top and eliminate the possibilities. First put some oil in until it is at the right level. Next check the battery voltage with a multimeter or take it in to any shop and they can check it. If you take it to a shop, have them put it on one of their discharge/charge machines and have the "health" of the battery checked. Old batteries can get buildups of lead sulfides that coat the plates and ruin the batteries.
But the sound you described makes it seem like the battery is fine. If the motor is attempting to turn over, you can rule out the starter as well. A messed up starter usually makes a whizzing sound. A clicking sound is a sign of a dead battery. If its turning over and not starting, could be a spark, fuel, or air issue. Unless you have a filthy filter or something dead in your air box its likely not this so spark or fuel. Spark problems come from dead coils, fouled plugs, computer issues, etc etc. Just start working your way through the different components and testing them to make sure they work.
Next thing to check is the fuel system. When you turn the key on listen for your fuel pump to turn on. You can hear it if you go outside of your car and listen by your gas tank (usually located inside or mounted to the tank). If you have a newer car with OBD2 you can pull up fuel pressure and all that jazz if you have a fancy scanner or know a shop or person that has one. If the fuel pressure checks out it could be a carb/injector issue. EFI cars usually have OBD2 and an injector issue would throw a code which would trigger the check engine light. If the light is on, pull the codes with a scanner and move on from there.
If this all sounds like a foreign language take your car to a shop! Hopefully its something simple to fix and you could either do it at home or take it to a shop and pay labor. A seized motor can be a bitch to fix because theres multiple things that can seize up a motor and a bunch of fixes. But again, if the motor sounds like its turning over when you crank it, it is likely not seized up.
Try some lighter weight oil as well. 10w or 15w oil in the winter is harder on the motor since its so cold and the oil gets really thick. Lighter weight stuff will work great in the winter and then you can move back up in the summer if it gets really hot.
