I did some reading in your 2002 Buick Century owner's manual and it says that if the security light blinks then clean the little bump on your key where resistor pellet is - that's what they call it anyway.
If the security light is solid it says that your key may be bad.
Do you have a spare key you could try? Also, you said that you unlocked the doors from the inside of the car. Have you tried locking and unlocking the car with the key fob - this might reset your security system and allow the car to start.
If you see a good spark then most likely you don't have an electrical problem. I would check the fuel system next. Unless you have the proper tools you probably won't be able to do this yourself.
I believe their is a green cap under your hood that protects the fuel regulator bleed valve. The valve is on the left (driver) side of the engine bay closer to the windshield. It's like letting the air from a bike tire but instead gas comes out - don't press the valve unless you have some rags and you protect your eyes. You can do this by gently pressing in with a small screw driver - it won't take much and it should give you a bit of a squirt of gas. If you let the pressure off that way and then try to start again - and then come back and there's more gas pressure there then it's probably not your fuel system. If no gas comes out then you probably have a fuel pump problem or something else to do with getting fuel from the gas tank to the front of the car.
Once you get there then we can try other things.
It doesn't sound like there is anything really bad wrong with your car - if you were just driving it and you didn't notice any lurching, lights dimming, didn't stop running on its own, bad sounds, bad smells, it could be something simple.
It doesn't mean that there's not something major it just doesn't sound like it.
Don't allow any mechanic to just start throwing parts at it in an attempt to fix it before he's adequately diagnosed the problem. If he's a good mechanic he'll make sure he's identified that actual problem. If you feel like the guy is pulling your chain then have it taken to another mechanic - it might take another tow fee but a shady mechanic can cost you a $1000 for a $50 fix.
You can always come back here and ask more questions. There are a lot of really qualified techs here that like to help others with their car issues.
Good luck and let us know how it's going.
