[geezer#99]

THere should be 2 wires on the solenoid. Left one is a purple wire that goes to the S terminal. It comes from the ignition switch. Right one should be yellow that goes to the I terminal. It runs to the coil.
When you turn the key to start the motor, power is sent to the S terminal from the ignition switch. THe solenoid pulls in, the starter cranks and your motor starts. Also when the solenoid pulls in a connection is made inside the solenoid and 12v is supplied to the coil via the yellow wire. You need 12v to the coil for starting only. When you release the key, power is shut off to the solenoid and then power from the ignition switch to the coil comes thru the resistor wire to the coil. Voltage is reduced to about 7-8 volts. You can't run 12v to a coil all the time or they overheat and quit.
If it cranks over slowly then definetly replace the battery cables. You need clean connections and good wire for cables. They may look good but can be corroded inside.