my car bogged down and then wouldn't start got it started only for it shut down completly
Could be a few things, Crank sensor, coil going bad, problem fuel pump. Check for spark, check for fuel. There could be a ton of things that could cause this. I would recommend that you take it to a garage.
The Century has very few problems. For one I would check the small vacuum hose running from the top center of your intake manifold , it is a small somewhat s-shaped hose. Every time this would fall off of mine, it would idle terribly and stall out. Could be your TCC (torque convertor clutch) solenoid, if you were driving...You will need a mechanic to check all possibilities though.
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