93 century stall, longish read

(Summary at bottom)
Hello guys. I've read a few of the other 93 stall threads and they didn't sound quite like my situation, so I'm making a thread of my own in case someone can give me advice.

Up until a few days ago my century had a few major problems. One was a loud rapid clicking noise under the hood whenever the engine was on. This was annoying for sure but it didn't really bother me. The other was the car's engine's tendency to stall whenever I stopped (only after going 36+ MPH). The engine would just outright die after the car shook a few times. In order to start it again, I would have to wait 30-40 minutes to pass then it would.

I took the car to a mechanic, and it turned out I had a ruined harmonic balancer. He told me the balancer was the reason the car made loud annoying noises. He put a brand new one on and I started the car and there was a lot less noise, but there was another noise I noticed. But I ignored it. I asked if the bad balancer had anything to do with the engine cutting off after going 36mph and he said it might.

So I'm driving home in my lovely lot-less-loud car, doing 44 (in a 45 zone) and the light ahead of me turns red. I slowed down and right before I got to a complete stop, the car started shaking a bit and poof. Engine dead. Could not get it to start, I had to wait a half hour (like before). Well, I called the mechanic saying nothing changed stall-wise and he apologized, and told me to bring 'er back. He did a free diagnostic and said the new noise I heard (paragraph 2) was being caused by a broken serpentine tensioner. He he said he would pay for it out of his own pocket and do the labor for free.

Fast forward to today, I go to the shop to pick up the car, start it, and a smile crosses my face. Zero noise under the hood, only the blissful hum of the engine. I wave to the mechanic and pull out of the parking lot and head home. The car was running beautifully (I was doing 40)UNTIL I came to a red light. Engine dead. Won't start. 40-cars-full-of rush hour traffic behind yellin at me to "get the %#!& outta da way!" Teenagers driving by shouting "Sucks to be you! Hahaha." A few people threw french fries, and one guy threw a shoe at my car. This was while I was moving it to the curb =/. Those french fries hurt btw.

I've had enough, this car is testing my patience and emptying my wallet and is embarassing. If anyone has any ideas, whether it is "Junk that piece." or "It might be the crank position sensor." Please respond =)

Summary:
1. If I stay below 35 mph, the engine will not die at red lights. Car runs fine.
2. If I go 36+ mph, the engine is guaranteed to die once I reach a red light/stop sign, and the car will not start for at least 30 minutes
3. The car has a new serpentine belt, new harmonic balancer, new water pump, new serpentine tensioner. (Old belt broke, old water pump was ruined).

The cps is a possibility since it takes 30 minutes to restart. There are two other possible causes. First, does the car have a security system and does the light come on when this happens? If yes then you need to have it reset or removed. If no, I would check the torque convertor lock-up solenoid. I don't know what speed the thing kicks in on the Century but if it is sticking it can cause the stalling you indicate although they usually don't take 30 minutes to reset. The reasoning behind the TCC solenoid is the fact that car only stalls after you reach 36 MPH or higher.
When you have some time and there is no heavy traffic, take the car out and speed up past 36, when you come to a stop sign or light kick the car into neutral when you feel it start to shake and see what happens, If it does not stall then the TCC solenoid is bad and needs replaced. A simple test to try to determine the problem. If the car stalls we will have to look elsewhere.

Thanks GTP I'll try that, there are a few dusty roads nobody uses around here that I can do that on. Thanks thanks thanks thanks.
Gotta get the car towed over here though heh. Oh yeah, no security system.

*goes off to read about TCC solenoids*

Oh lord I'm stupid. I forgot a major detail from the first post. After the engine dies(after going 36+ mph) the car can actually start again. The engine will run as long as I keep it in park. Once I try to put the car into drive however, THAT's when the engine dies(again). What I meant to say in the first post, was that I have to wait a half hour before I can shift into drive without the engine dying. So sorry I left that out b/c that's a major detail =/.

I had a similar problem with a GM product that the TCC would not release. I finally unplugged it and the problem went away. I replaced the solenoid and the car ran fine.

The other possibility is that speed sensor in the transmission is bad. These things can cause cars to do strange things. You may want to look there too.