Car engine dies while at red light or standing still...

This is a 2002 Mercury Grand Marquis by the way.

First thing that comes to mind is that there may be something hooked up wrong like vacuum lines. How about the timing?

I was told to get the vacuum lines checked. Are these all signs of timing problems?

Only if it is way off. Was the distributor moved?

It was not

I used Autolite spark plugs and I was now told that the plugs should have been gapped but the person who put them on for me was not sure if they were gapped, just by inspecting them

Then a nay on timing. How was it running before you changed the intake? Why was it changed, and back to original intake?

The original intake was leaking antifreeze, so I changed it out. Before this it was not cutting off

That is why I changed all spark plugs and coil packs

Auto light spark plugs are normally gaped pretty close to what they are suppose to be, but would double check afterward, don't think that is the problem unless they were way off. Three things to do... check vacuum line routing...take some carb cleaner and spray along the intake gaskets having the engine idle at a steady rpm, and around throttle body, anywhere there is vacuum, if there is a leak the rpm will pick up...and put a scanner on it to see what codes are there, Reading these codes will point you in the right direction. You can post them here so I could analyze these.

Yesterday I put it on a machine at autozone and it said replace coils and spark plugs, but I had already done so. I was told the reason that was because the check engine light had not been reset after putting on new coils and plugs.

Does it seem as if it may be the timing after giving you all this information

Ya but was it? If it was reset then there is a new set of codes. Check engine light is on for a reason.

Never hurts to check the timing. There is a crankshaft sensor and a camshaft sensor. Thats why I'd like to know if there are new codes. These two sensors affect the timing and how the engine runs.

The check engine light has not been reset after putting on new coils and spark plugs

So do I need to reset it and then put it back on a scanner

Codes need to be reset since you did a fix for them. Check out the other things I mentioned above first, It's just that if we had a new set of codes that would point us to the right direction of a fix. I believe you just may have something not hooked up or plugged in, or a vacuum not hooked up right. Don't get hung up on the codes until you do some checking. Resetting the codes is not going to fix the problem.