1995 Satun Twin Cam wont turn over
 

I was driving my Saturn on a relatively cold day here in MI, and it just shut off and I coasted over to the side of the road. It may be incidental, but the heater wasn't working for the first time the day before. Other issues the car has is a small leak in a radiator hose (which I was preparing to fix) and it burns oil, so I've been using additives to correct that.
When I came back to the vehicle to jump it, we could hear the starter clicking but the engine wouldn't turn over. The battery seemed fine, seemed to hold a charge for a bit from the jump attempt and the lights worked great after leaving it hooked up for a couple minutes. Another attempt to jump it had the same results...all the electrical worked fine and so on.
Checked all the fuses, they seemed fine as well. The starter was replaced within the past month and I can hear and feel it clicking. The fact that the engine isn't even trying has me wondering though.... it has been smoking consistently for a year and I wonder if something finally just broke inside it.
Any insights? I'm at my wits end, not really being a car enthusiast.

Is it a single click of the starter solenoid engaging (but the engine not turning) or a chattering click at the starter (with the solenoid not fully engaging)?

As the engine is not turning over, my first inclination would be bad battery or corroded/loose battery leads, but you indicate electrical seems fine, and usually your charging light will come on if the battery is no longer holding a charge.

Based on the smoking (oil going into combustion chambers= oil not lubricating engine), and coolant leak (= cooling system not fully pressurized= cooling system not removing heat from engine as designed), and your heater not working the day before (= water pump probably failed and was not circulating coolant through the engine), my guess is that the engine seized due to lack of cooling.....

Hope I'm wrong.

How low is the coolant and how low is the oil?

Engine HAs most likley seized to test this theory take a socket and place on the cranshaft balancer bolt and atempt to turn the engine by hand if you can not turn the engine by hand you need a new motor

Yeah, I'm pretty sure that is what happened... you guys have affirmed my suspicions (from talking to some mechanics and the like). Located the nut I have to turn, but haven't tried it yet (there is a lot of snow falling around here!). Thanks for the advice... it was pretty close to needing a new motor anyhow. My plan is to get another vehicle and then fix this one to work as a backup, which if I'm lucky won't involve getting a new motor, but if it does, so be it. I was already pretty close to this point anyhow. Again, thanks for the info! I'll get to working on it in the next month or so and give an update. My only hope is that I didn't hear it grind or make any loud noises when it stopped running, so it might just be jammed up.