What could be burning out my solenoids and motor not turning all the way over at times

If your getting constant voltage across the large solenoid terminals it is stuck in the 'Live' position giving continuous power to the starter motor. There is a chance this has burned out the starter motor.
You need to "Bench test" the starter to see if it still turns. This is where you completely remove it from the engine to check it.
Clamp it TIGHTLY in a bench vise if your doing this as these thing jump when you apply power.
First check is to turn the drive cog by hand. A good starter will turn smoothly and quietly with just a little bit of resistance. Any grittyness, noise or notchyness and the motor is bad. If it spins smoothly you can test it with live voltage. AGAIN Recheck it is tightly gripped in the vise! For NO MORE than 2 seconds apply 12 volts from a MOTORCYCLE battery to the large terminals on the starter motor. A good motor will suddenly spin really fast as soon as you apply power. Slow, noisy or no reaction means a bad starter motor.

Solenoid burning up usually is due to either starter motor drawing too many amps, or factory cables being too small gauge wire.

First make sure you have good battery connections. A poor connection will give enough power to turn on head lights but not turn on starter motor. Clean the connections and ensure they are tightened.

If connections are good, check voltage of battery. It should be at least 12 volts.

If battery voltage is low, either charge the battery, or attempt to jump start the car (red to positive terminals, black to negative terminals; attached positive first, prefer to attach negative terminal to a good metal location other than the negative terminal on the battery).

If the starter motor is visible, try tapping lightly with a mallet to free it up. This may or may not work depending on the problem. If the car starts, replace the starter motor anyway or it will strand you again.

Most cars have a starter relay and a fuse for the ignition. Do a Google search on the internet for your model of car, or look in your owners manual to find the location of the solenoid and/or fuse. Replace the fuse if it's burned out. Note that a shorted starter motor could cause the fuse to burn out, so replacing the fuse may not fix the problem. Suspect a shorted starter motor or wire if the fuse burns out again. You may need some professional assistance at this point to check the solenoid.

If the solenoid is bad, it is usually replaced along with the starter. Remove starter motor/solenoid and take to an Autozone or Oreilly or equivalent and have them check its functionality. Be sure to disconnect the battery's negative terminal before removing the starter motor.

If the starter is good, then your problem is likely either your car's security system (check if security light is flashing if you have such) or check the ignition switch. If you have a mechanic friend, see if he can bypass the ignition switch and get the starter motor to turn over.

Poor electrical connections or a bad battery or a bad starter motor/solenoid are the most likely culprits.

Two parts to this circuit, the low current: power supply to the ignition switch which then passes to the small wire on the solenoid when you turn the key to the start position, at this point there should be an audible "click" from the solenoid. Don't forget the solenoid needs an earth to operate, so check the earth path too, usually through its attachment point(s) Check that the ignition switch has power going to it. Check that the power is transferred to the start wire when the key is turned. Check the power is arriving at the solenoid, small wire. Check the solenoid has a good earth. Does the solenoid "click" when you try to start? Yes to all this? Then the low current side is good. The high current side: a permanent live (hot) to one side of the solenoid. When the key is turned to the start position and so long as the solenoid "clicks" then the power to the permanently live terminal is transferred to the other high current terminal. If it is not, then the terminals inside the solenoid are burned/dirty/high resistance. You might be able to dismantle, else change the solenoid. If the power does transfer, but the starter motor does not turn, then suspect the starter motor itself. Check there is a good earth for the starter motor, the heavy duty cable to the engine is in good condition, terminals clean and tight etc. If all good, then the starter motor is most likely U/S.

There are four things to check:

1. Battery cables to starter and ground. The connections may be loose or corroded. In particular, if you have a replacement clamp on the battery end of the of the cable, check for corrosion buildup at the clamp/cable connection.
2. Check for voltage on the solenoid coil terminal with the ignitions switch in start position. If you don't get any, you may have a bad start contact in your ignition switch.
3. If you consistently get voltage on the solenoid coil, but the starter doesn't run, you have a bad solenoid or
4. Worn-out brushes in the starter motor.

You may hear the solenoid pull in when you turn on the starter, but have no motor rotation. This could still be due to a bad solenoid; the contacts for the starter could be burned out. This is the most likely cause of intermittent operation. The contactor element looks like a giant copper nail; the solenoid pushes the head into two posts (one connected from the battery, the other to the motor). If part of the head is burned out, it won't work when that part faces the posts, but if the contactor jiggles around until two good spots hit the post, you can get started.

If, when the switch is turned, the starter motor does not operate at all but the solenoid clicks, the problem lies with either the battery, the main solenoid contacts, or the starter motor. If, as you say, the battery is good, and fully charged, that would mean that is was either the solenoid contacts or the starter motor.
If the solenoid plunger cannot be heard (no click), the battery is bad, the fusible link is burned, or the solenoid itself is defective. Once again, if the battery is good, it would be the fusible link, or the solenoid. The fusible link (battery fuse) is in the engine compartment fuse block, fuse number 1, 80A.
If you want to test the circuit, you can run a fairly heavy INSULATED wire between your pos. battery post and the SMALL terminal on the solenoid (just touch the end to the solenoid). If the starter turns, you may have a ignition switch, neutral start switch, or some other wiring problem.
Double check the battery terminals to make sure that you are getting good contact.
Hope this is helpful.

If, when the switch is turned, the starter motor does not operate at all but the solenoid clicks, the problem lies with either the battery, the main solenoid contacts, or the starter motor. If, as you say, the battery is good, and fully charged, that would mean that is was either the solenoid contacts or the starter motor.
If the solenoid plunger cannot be heard (no click), the battery is bad, the fusible link is burned, or the solenoid itself is defective. Once again, if the battery is good, it would be the fusible link, or the solenoid. The fusible link is in the engine compartment fuse block (the box on the upper left as you face the vehicle). It is either 80A or 100A.
If you want to test the circuit, you can run a fairly heavy INSULATED wire between your pos. battery post and the SMALL terminal on the solenoid (just touch the end to the solenoid). If the starter turns, you may have a ignition switch, neutral start switch, or some other wiring problem.
But, first, just because the radio plays or the lights seem to work, that does not mean that the battery is fully charged and can handle the load of starting the car. You might try jumping it from another car, or putting a charger on it for a time. If you decide to take it out, make sure that, if you have an anti-theft radio, you have the code to reset it.
Hope this is helpful.

don't need the fuse, have your battery testes with any auto parts store for free (auto zone) making sure your battery still have the cranking amp to turn your starter over, if not than replace it; next, if the battery are good, your starter may be bad, solenoid which act like a switch to the starter motor usally burn out before the motor does, and you may need new starter, new will cost you 140 bucks or so, you can get a rebuilt one for about 75% of the cost new. ebay or junk yard might be even cheaper.

If, when the switch is turned, the starter motor does not operate at all but the solenoid clicks, the problem lies with either the battery, the main solenoid contacts, or the starter motor. If, as you say, the battery is good, and fully charged, that would mean that is was either the solenoid contacts or the starter motor.
If the solenoid plunger cannot be heard (no click), the battery is bad, the fusible link is burned, or the solenoid itself is defective. Once again, if the battery is good, it would be the fusible link, or the solenoid. The fusible link is in the engine compartment fuse block (the box on the upper left as you face the vehicle). It is either 80A or 100A.
If you want to test the circuit, you can run a fairly heavy INSULATED wire between your pos. battery post and the SMALL terminal on the solenoid (just touch the end to the solenoid). If the starter turns, you may have a ignition switch, neutral start switch, or some other wiring problem.
Your alternator is not the problem.
Hope this is helpful.

this car uses a Nippon Denso starter, this click means the heavy electrical contacts in the starter mountedr starter solenoid are burned, the solenoid works (the click u hear) but because of the burned contacts the starter gets no power to engage, u can replace the contacts only for around $15 from the following link, u will need the starter motor number.

http://www.iowamotorparts.com/index.htm