Starting / Cranking is a problem: With key ignition, turn; there's a slient buzz noise. Head lights and dash board lights come on, however it doesn't respond to crank. Weak response is battery sometimes requires charging before attempting to start the engine. Suggestion are appreciated.

check and test battery-fuses-relays most likely dead battery

If the engine cranks but won't start an run why do you want to mess with the starter ?
2004 is cranking but won't start or turn over ?????? What happens when you turn the key to the start position ??? Does the starter engage an spin the engine around or nothing happens ???? This would be a no crank no start condition . Does the little red light on top center of the dash flash fast while trying to crank the engine ? Anti-theft system (PATS) problem if it is flashing . Your best bet , mite be to take it to a qualified repair shop.

Check all cables to battery especially the ground negative cable.

With very little to go on here i would say crank sensor or ignition timing out of alignment check timing marks if ok check crank sensor connection at the bottom of the engine

The ignition switch is not reading the chip in the key, Triggering the anti-theft mode in the ECU.

Thanks for choosing FixYa and welcome. When you first turn the key on, you should hear your fuel upmp kicking on. It is a soft buzzing sound that last for two seconds. Turn the key to on and listen carefully. Put your head toward the back seats. Make sure there are no noise so you can hear it clearly.

The way to approach this sreies of issues is to first remove the remote start/alarm from the equation and restore the vans electrical system back to original. From there, if it persists, we can do more trouble shooting. Let me know and I can walk you through the process. This is definately a problem that does require a diagnostician. Thank you for the level of detail you provided!

the battery says 12 volts but may be dropping to 4 or 5 under a load...i would suggest jumpstarting the car and see what happens.the battery should read in the high 12 volts and not less than 9.5 under cranking. the dash lights go out on your car when starting,and the alarm will go off ,and disable the ignition if the voltage is too low in cranking the car because the computer will shut it down and activate the anti theft.....check your battery posts are tight. best of luck

Electrical problems are difficult to diagnose in person without testing ...however, it seems that you may be loosing the body ground, causing power loss to the clock and likely the computer as well. As the starter is able to turn the engine, likely there is no problem with engine grounding. While cranking, the accessory side of the ignition switch should remain "hot" otherwise you would loose the clock every time you started it up. If it's not a ground problem, I'd look at the ignition switch itself to make sure it's not dropping power to ignition system while starter is engaged. on some vehicles this can also happen at the starter relay if an ignition bypass is used to provide hotter starting spark.

try over riding the starter relay on the fender ,it has one there right?. dont go to a mechanic yet. the engine aint seized. if it doesnt have this relay then i would get the alternator tested. if you want to test it yourself it can be costly for the right equip. autozone usually tests for free. i dont know were you live so if theres not an autozone. let me know if you cant get it tested.