If your new coil requires a ballast resistor, you should install one. The reason for this is to prevent the points from burning up from the 12 volts (measured at the + terminal on the coil). The resistor will keep it down to about 9 volts. Sometimes it is easier to just install a coil that has the resistor built-in. If your coil needs one, just go down to the local auto parts store (not a "chain" store, they may not know what you need) and pick one up.
As for the starting trouble, make sure your battery is fully charged, all connections are clean and tight and most of all; check your grounds! This is the most overlooked item when there is a starting/cranking problem.
Also, if your positive cable gets warm or even hot after just a few seconds of cranking; you may have a bad starter. Brushes and bushings are cheap and you can install them youself without much trouble. The solenoid is really easier to just buy new (if the brushes are good and the bushings are tight and the starter checks out otherwise), they are fairly inexpensive also.
