Toyota Repair: 87 Toyota Van starting problems, ground cables, damp weather

Question
My van with 4YEC engine has developed a couple of starting problems, both electrical in nature. If it's warmed up and I shut it off, then try and restart about 10 to 20 minutes later, the solenoid will just click.  If the engine has cooled down, or if I try to restart right away after shutting it off (when hot) it will crank over and start just fine. It has a rebuilt (Bosch brand) starter motor in it that's about a year old.
Also, it has a weak or no-spark condition sometimes in very damp weather and cranks but won't start... should I get a new coil?  

Answer
The starter clicking noise is usually due to a bad solenoid, it couls also be caused by corroded battery connections or a voltage drop in the wires from the battery, make sure all the ground cables are attached and tight.
The starting problem with the weak spark may be caused by the coil or the spark plugs, the plug wires or distributor cap and rotor, if those are original or old, I recommend replacing those to see if it helps.