I have a 2002 Lincoln LS V8 with about 80,000 miles on it. I bought it several years ago with about 18,000 miles on it. The problem I'm having is that occasionally the car just will not start. It is very random, but the car is always cold and it seems to happen more frequently when the weather is cold, but it has happened in the summer as well.
When this happens this is how I get it to start. I pump the gas a whole bunch of times and then hold the pedal to the floor for a minute or two. If it doesn't start, I repeat the process. Sometimes it takes 2 or 3 times before it starts. After it starts, all is well.
Your description is a near-miss in comparison to cold-start problems dealt with by a Ford technical service bulletin. I ran across TSB # 03-7-3 with the ALLDATA information system.
This one deals with a hard-start condition due to flooding, but only -- I repeat, only -- if the problem occurs with ambient temperatures between 30 and 40 degrees F, and humidity above 75 percent. Sounds like a cold rain, to me.
The fix for the 2002 model year LS (V6 or V8) is an updated calibration for the powertrain control module (your engine's computer). But you said it also happened in the summer, and the bulletin is very specific as far as "not" using this fix if the problem occurs anywhere outside the specific temperature and humidity parameters.
If it is cranking away in a warmer/dryer climate, move on. Possible causes are then wide spread. The IAC valve, which controls idle speed, is on the list, but that's where another bulletin comes into play. Ford TSB # 03-3-5 deals with accurately diagnosing, or not, the IAC valve as the cause of the problem. Aside from that, an intermittent extended-crank can be caused by ignition issues, too much or too little fuel, so on and so forth.