THANX! for posting what you found ... 

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Thank you all for the advice on the solenoid. I decided to throw money at it and installed a new solenoid and the problem was solved. The engine now fires quickly and consistently when the key is turned to the start position. I decided to do an autopsy on the old solenoid. I shaved off the 4 rivets and pulled off the metal backing plate and pulled out the plunger that moves ever so slightly when you turn the key. I discovered a thin copper tab that fastens to the internal connection of the I post. It looked like the copper tab had developed a stress crack and had finally broken loose after moving several thousand times with the plunger. I guess my I terminal had not been sending voltage to the coil. Hard starts on a cold morning were the most pronounced symptom.

Hoosier Hurricane nailed it.  If this problem is recent you need to check your wire connections.  Connect a test  light to the “I” terminal on solenoid you should get power in start.  No light on I terminal in start, replace solenoid.  

The easiest way out is to install the points and condenser (if kept) (don't buy new as it is junk) and see what she does. Otherwise you are going to have to go through a diagnostic routine.

This has been happening since original install and the problem was not there with points?

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Has this been the same since you put in the Pertronix ?  If so, it is wired wrong.  I had the same problem with a conventional distributor (Mallory) many years ago and found out I had it wired wrong.  Unfortunately, I do not remember what I did wrong (at that time I wired up my 48 (302) with an aftermarket harness)..    If you don't have the original directions, get hold of Pertronix and ask for a copy.  They may have one you can download.

54 Victoria 312;  48 Ford Conv 302, 56 Bird 312
Forever Ford
Midland Park, NJ

Geo56, if your Pertronix 1 lasted 15 years+, I would say that you got your money's worth. A family member has had a Pertronix 1 in his 65 Mustangs for years without issues. You might consider replacing it with the Pertronix ll, if it's time, but the Pertronix lll, I don't think, is compatible with the 57 distributor. 

I am using the 57 and up distributer.

Are you using the 1956 LOAD-O-MATIC or 1957/ DUAL ADVANCE DISTRIBUTOR?

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I believe I have the Ignitor 1 as it was installed over 15 years ago. I am using the original resistor.

sounds like something is not wired correctly..  What Pertronix, one or two. and are you running the resistor?  If two, then the resistor need not be used.  The brown wire is not used if you are not using the resistor

54 Victoria 312;  48 Ford Conv 302, 56 Bird 312
Forever Ford
Midland Park, NJ