My 2003 Honda Element wont start on wet/foggy mornings. If I put it in the garage or a blanket/tarp over the hood, it will start; with a few cranks but it starts. First they checked the battery, it was low. Then I was told I needed a new starter. This has been happening intermittenly for about 4 months. Any clues? Could it be moisture under the distributor cap?

When you park your truk at night,the engine is warm/hot.Now its start to cool down.In doing so,condensation collects under the hood and around the cooling off engine.The condensation freezes,making everything wet,including the wires.Tht's why its hard to start in the morning.
Trick is: when engine is parked and off,place a heavy blanket over the engine,close the hood.The blanket will absorb any condensation.Just remember to remove the blanket in the morning before you start the engine.

Are there any lights lit up on your dash?? This sounds familiar ... The security system sounds like it is failing which is a very common issue in GM's. There is a module that you can get to bypass it.. you can even put the part in yourself.. read this over and see if you think it will help..

Pull the plugs out crank the motor a few times then put them back in

By plugging it in I assume you mean the block heater for the engine.
I would plug it in for an hour or two before starting. also give the glow plugs plenty of time to heat up before starting. If you don,t have a garage to put it in try to find a place out of the wind and with direct sun in the day this may help some. laying an old blanket or quilt or even a tarp over the hood and front end could help some. after sitting for a prolonged period of time in cold weather hook a charger up to the battery before starting to top off the battery's charge. Hope this helps.

Change your starter.

waterproof the engine compartment, moisture is the most likely cause

Sounds like moisture getting into a wiring connector.
Someone will need to check the electrical system to find the source of the problem. They may be able to spray water on the engine to duplicate the condition, or you may have to leave it outside the shop overnight.
You'll need to know if you are missing spark to the plugs or fuel pressure to proceed.

If it cranks but won't start, the alternator would not be a concern.
Have you checked spark, fuel, and compression yet ?

spray your distributor wires and cap with silicone spray. If this does not work you will have to replace distributor cap as it will have a hair line crack in it.

Good Morning,
Check for moisture in the Distributor and use a blow dryer to dry it out. You may want to consider changing your Spark Plug wires to a "Moisture Resistant" type. Please let me know if this helps you and thank you for using FixYa!