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I'm not familiar with your specific vehicle, but some things that can cause this are a high idle speed, worn or broken motor or transmission mounts or low transmission fluid level. If all these are ok, then you can look into flushing the transmission fluid and replacing the filter.
The TOD light flashes when a code stored in the TOD system. You will need to have a shop pull the codes and diagnose the fault.
When a vehicle cranks over, but doesn't start, there are several things that can cause this. You need to check for the appropriate fuel pressure and make sure the injectors are firing properly. The ignition system needs to be checked to see if the spark plugs are firing, and that the timing is correct. In addition to these things, the engine timing needs to be checked. You can start by checking trouble codes and see if any are stored as this may help direct you to the cause of the problem.
When the plastic "neck" of the radiator is broken, then you will need to replace the radiator. Be very cautious when it comes to the cooling system, overheating the engine will do thousands of dollars in damage very quickly!
You will need to look at the owners manual for the fuse location. You may want to look at the brake light switch, if for some reason the shop was working in that area, they may have bumped the switch and affected the adjustment, causing the brake lights to stay on.
It's important to see if any of the pulleys are out of alignment, if so, they will need to be corrected. If all the pulleys are aligned correctly, then look at the condition of the belt, if it has cracks, then it should be replaced. If the belt appears OK, then it may be glazed or contaminated, or you may have a bearing in one of the pulleys that is starting to fail.
If the engine is shutting off instantly, then it sounds like you may have an electrical component that is shutting off. This could be a relay that controls the fuel pump, the fuel pump, or an ignition related component. It's unlikely related to the fuel filter, or the charging system. Have a shop check the trouble codes for you and see if any codes are stored, this is a good place to start.
So when it's under 40 degrees, the engine is cranking over, and the fuel pressure is zero? Have you checked for any trouble codes?
You'll have to have the codes read out to determine the cause. Could be a low battery voltage, bad ABS sensor or a bad control module, but without the codes, these are all just guesses!
A Check engine light can come on for many many reasons. The first step is to check the codes, before that you can perform a visual check of the wires and hoses, but that;'s about it. If you can get the codes and post someone can give more info.