I'd say it makes a bunch of difference! Sorry to tell you, but your Pertronix may be dead. If they are left switched on for any length of time with the engine not running or the distributor not turning, the coil can overheat and this in turn damage the ignitor.
However, let's be positive and hope that's not the case. You should have a two wires going to the Pertronix, connected to the low-voltage terminals on the coil. It is vitally important that these are connected the right way round! I have heard, though don't know for certain, that if you connect them the wrong way you burn out the ignitor pretty quickly. Assuming your car is negative earth, the red wire for the ignitor should be attached to the + terminal of the coil - the same one as the white wire you mention - and the black wire to the negative terminal.
Do you have a test lamp - a simple bulb in a holder with 2 leads so that the bulb will light when you have a circuit? If not I suggest you get or make one, then connect one side of the lamp to the distributor side of the coil (with the black ignitor wire) and the other side to ground. With all wires in place, ignition on, operate the starter and the light should blink on and off.
I can see why you didn't respond to posts above that talk about points and sparks and stuff - you have no points to spark!