95 LHS: Hard starts when cold

Just yesterday, I acquired an old 1995 Chrysler LHS for next to nothing ($500). Just needed brakes and new tie rods and an alignment. Also need to replace the trans pan gasket, it leaks about a quart a month.

It has an aftermarket remote start/security system in it. Yesterday and early this morning it starts up perfectly (it was cold this morning). 8 hours later, I go to leave work and I pressed the remote start button and got to the car and I hear the blower motor running but no motor.

I turn the key to start the car myself, it cranks and cranks and cranks. Tries to catch but no go. I hit the gas to open the throttle thinking maybe the car has an IAC (I know nothing about the specific motor design of an LHS yet) and it catches a little harder this time but doesn't start. I let it sit for a bit and try again and this time it starts after a few tries, runs slightly rough for a bit (about 30 seconds), then smooths out. I was able to drive it home without ANY issue. It also will start up perfectly fine just after shutting it off.

If it has an IAC, could this be? O2s? Plugs?

A buddy of mine mentioned it could be sticky injector(s). Would that fit the bill? It would seem to make sense to me that since as they warm up, they behave more normally.

My next steps:
-change fuel filter
-check pressure
-check injectors (what's the best way? just listen for clicking through a screwdriver or something?)

I just went out and started it cold this morning; starts perfectly. Could the remote start be doing something different? I don't see how.

Would low ATF cause this maybe?

I am repairing the trans pan gasket on Thursday and will also be replacing the fuel filter and checking the pressure then.

I would assume that, just like with my Crown Vic, if fuel pressure is the issue, opening the throttle of course affects the TPS which will supply more fuel, which is why I can get it to start roughly by pressing the accel. Assuming there is a fuel pressure regulator, I may want to check that as well, no?

Fuel filter is cheap, so like I said, I'm going to do that anyway. If pressure is still low after that, I will replace the regulator. If still low, will replace the pump. If I still have starting issues, I will check the injectors. Sound like a good plan?

I noticed a small coolant leak also. I haven't investigated too much yet but it appears it is coming from a freeze plug on the plug a little behind the water pump. Will this require engine removal to replace the plug or can it be done from below? When I looked underneath the car it appears there is very easy access to this area, but appearances can always be deceiving.

I should've mentioned in my first post that there is no CEL either, unless the bulb is burned out. :-P Thanks for your replies, too.

I think I found out why this whole issue was happening... I only truly noticed it happen after I tried to do remote-starts before. The remote starter only cranks the engine very briefly (one second), and the couple of times it did this, the motor didn't catch, however the fuel system was still dumping fuel into the CC I believe.

I went to start it up again and it was cranking over and over, finally caught, ran rough and black smoke came out the exhaust and smelled of raw fuel. Motor was "flooded". After about 10 seconds, everything was fine and it ran like a champ. Needless to say, I'm going to start it "manually" for the next week and if I have no issues, then I know exactly what the problem is and I'll have the remote start programmed to instead do a 2-second crank on the starter.

As for the water pump/coolant leak, the previous owner says the WP was already replaced, but now I wonder... I am going to pull the cover and see where it's all coming from though, it's either going to be the core plug or the WP. According to a few sources, some minor coolant spillage out of the weep hole is normal in the 3.5, under certain conditions, is this true? I wonder if a) it was overfilled when the water pump was replaced or b) I ran it too hard when I was trying to start it the other day and some spilled out.

Well, I guess it isn't the remote start. Went to start it today and crank-crank-crank... Finally started up with the same thing I described before. Black smoke/fuel smell.

Someone from another forum posted a TSB on this issue (the site is down for maintenance otherwise I would post it), has to do with choice of spark plugs and PCM programming on early 3.5s preventing it from starting in freezing temperatures.