I have a 2003 Mitsubishi gallant 2.4. it will not crank: no noise. have power at the starter and at the solenoid when switch closed, new battery, new starter, new ignition switch. electrical connector at solenoid reads 12.4 (a slight drop in voltage) when switch engaged. what else could it be?

The most likely reason would be bad contacts on the starter relay or starter solenoid. You aren't getting enough amps to the starter.

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Not necessarily. You may simply have a bad connection at the battery or at the starter solenoid. You could also have a grounding problem at the starter or at the starter solenoid. Or you could have a failing contact in your key switch! When you try to crank the engine, but it does not crank, do you hear any clicks or any kind of rattle sound or buzz? If you hear a click but no cranking of the engine, then you may have a bad starter solenoid ... which, if available, is a lot cheaper than a replacement starter!

I'm assuming just by the fact you had a new battery and new starter that sometimes when you turn the key to the start position , nothing happens . Is your vehicle a automatic transmission ? When it doesn't start have checked for battery voltage at the starter solenoid S terminal ? Is there B+ voltage at pins 30 & 86 for the starter relay ? Pin 86 while cranking the engine or trying to crank the engine over . Pin 30 check with key on . Try moving gear selector to neutral . Videos on youtube for basic automotive electrical testing . How to voltage drop test starter motor circuit Find a wiring diagram at www.bbbind.com
Starting System Circuit Description
Voltage is applied at all times to the ignition switch from the IGN A fuse 6 through CKT 242 (RED). When the ignition switch is turned to the START position, voltage is applied to the CRANK fuse 8 through CKT 5 (YEL). From the CRANK fuse 8, voltage is either applied to the clutch pedal position switch (M/T) or the transmission range switch (A/T) through CKT 806 (PPL). When either the clutch is disengaged (M/T) or the transmission is in park or neutral (A/T), voltage is applied to the coil of the starter relay through CKT 1035 (PPL/WHT). Since the starter relay is permanently grounded at ground G105 through CKT 150 (BLK), the starter relay energizes.
Voltage is applied at all times to the starter relay contacts from IGN A fuse 6 through CKT 242 (RED). When the starter relay energizes, the starter relay contacts close, and voltage is applied to the starter motor solenoid. Since the starter motor solenoid is permanently case grounded, the starter motor solenoid will energize two coils. The pull-in winding coil energizes in order to pull the starter motor solenoid contacts closed. When the contacts close, a plunger on the contacts causes the pull-in winding coil circuit to open. The hold-in winding coil then holds the starter motor solenoid contacts closed. Voltage is then applied to the starter motor from the battery through CKT 1 (BLK) and the closed contacts of the starter motor solenoid. Since the starter motor is also permanently case grounded, the starter motor will run until the ignition switch is moved out of the START position. When this happens, a spring in the starter motor solenoid moves the starter motor solenoid contacts and the plunger back to the rest position.

Check the starter solenoid and the connections from the battery to ground, battery to fusebox, ignition key switch, neutral or park safety starting switch, solenoid, and solenoid to starter. Make sure you have ignition key switch wires connected to the solenoid - without them - the solenoid can not close to send 12V to the starter.

Starter relay is actually mounted on top of the starter. Have you checked to see if your "new" battery was fully charged? If it is, then i would try a new starter which comes with a new starter relay. If you don't think its any of the above, it must be your starter switch. NOTE: starter switch is not where you put the key in, its mounted somewhere on your column, maybe even close to the floor and is actuated with a rod. You can actually start your car without a key after you find where the switch is located. Just pull down on the rod. (little known fact you can start a car without a key this way, hope your not a car theif, you can steal anycar this way lol)

Do warning lights and gauges come on, when key is turned to on?
If yes, check for power on the small wire at starter solenoid mounted on the starter with the key held in start. If power at the solenoid, take starter off and test for a bad starter or solenoid. If no power at solenoid when key held over to crank, work back to the switch in the start circuit-starter relay, clutch or neutral safety switch,-power from the start wire out of switch is not getting to the starter solenoid.
If no warning lights or gauges work with key in on position, power is either not getting to switch (bad maxi-fuse or fuse link, or bad battery connections-clean and tighten, recheck)-or the switch itself is not sending power out. Check if battery is charged up. Check all connections and grounds for loose, poor connections.
The start circuit starts at the battery, then to ignition switch, then out of ignition switch on the start wire to the clutch switch (or neutral/park on automatics), and on , ending at the starter solenoid on the starter. Somewhere in your starting circuit, power is lost. Start at the battery-check charge, check connections, check ignition switch.

Perhaps the thick power cable to the starter is broken. Is it a little click like a relay or more of a clonk like a solenoid? The starter often has the solenoid built in. It's this clonk that connects the heavy power to the motor. You don't usually notice this clonk because it's immediately followed by engine cranking.

So two possible causes;
1. Big power wire to the starter
2. Solenoid not firing.

load test battery
check for tight, clean connections at battery
check neutral safety or clutch safety switch
check starter relay
check ignition switch
check engine and chassis grounds,
below is from the autozone.com site. click on red X's to view files

Four types of starter motor are utilized depending upon the vehicle transaxle and assembly plant location. Manual transaxle equipped vehicles utilize a conventional starter motor which consists of a yoke, an armature assembly, an overrunning clutch assembly, a solenoid, a commutator end cover, a brush holder and a pinion drive lever. Automatic transaxle equipped vehicles utilize a reduction type starter motor which has, in addition to the components found on conventional starter motors, a reduction gear and shock absorber assembly.
In the basic circuit, the solenoid windings are energized when the ignition switch is turn to the START position and the clutch start/neutral safety switch is closed. The resulting plunger and shift lever movement causes the pinion to engage the engine flywheel ring gear. This movement also causes the starter solenoid contacts to close.
With the contacts closed, the starter solenoid provides a closed circuit between the battery positive terminal and the starter motor. Because the starter motor is permanently grounded to the engine block, the circuit is complete and cranking occurs as soon as the starter solenoid contacts are closed.
When the engine starts, the pinion is designed to overrun and protect the armature from excessive speed until the ignition switch is released from the START position. With the ignition switch released, a return spring in the solenoid assembly forces the starter solenoid contacts open, breaks the circuit between the battery and the starter motor, and disengages the pinion. To prevent prolonged overrun, the ignition switch should be immediately released upon engine start-up.
See Figures 1 and 2

Fig. Fig. 1: Electrical system diagnosis - No cranking condition

Fig. Fig. 2: Electrical system diagnosis - Slow cranking condition

check your postive and neg,cables to the starter ,if there is alot of corrision on the wires you wont get a good signal

ignition relay if good ===ignition switch.