Ground coffee will not dispense

the add beans to hopper signal most likely is triggered by the machine not sensing enough load put on the grinder (hence it thinks its out of beans) , this most likely is set by the grind (fine/course ) id say the grind is set to an improper size and the automatic sensor is picking up on that
another thing is the coffee / if its way too moist and not dry enough then its also going to trip the sensor as well

Think the grinding mechanism is jammed with something. Disassemble unit and look for same.

Clean your burr mill before using it for the first time. Then, to ensure optimal mill function and durability, clean it regularly following these simple steps.

1. Always unplug your burr mill after use and before cleaning.
2. Open the hopper lid. Empty any whole beans from the hopper. Remove the top burr mill by rotating it clockwise. For better results hold the grind setting button while rotating the burr mill clockwise. This will allow you to clean the grinding wheel and the grinding compartment.
3. Clean the interior recesses with a soft brush. Note: Never use water or liquid for cleaning the lower grinding section of this appliance. BRUSH NOT INCLUDED.
4. Wipe the whole bean hopper, its lid and the mill exterior with a damp cloth.
5. The ground coffee chamber and lid can be washed in mild detergent and water. They both are top rack dishwasher safe. Do not immerse the mill or the whole bean hopper in water or any other liquid or place in dishwasher. Use only non-abrasive cleaners to remove stains.
6. After completely drying the whole bean hopper and top burr mill, replace the burr mill in position by aligning snaps with receptacle and rotating counterclockwise to lock it in position. For better results, hold the grind setting button while rotating the burr mill counterclockwise. Once the burr mill is in position, pull gently to check it is properly locked in position. If the burr mill comes out, repeat this step again.
7. Replace the ground coffee chamber and lid, making sure both snap securely into place.
8. Fill the hopper with whole beans.

Are you talking about the coffee brewing system? Or the coffee grinding system? You said "gears" so it sounds like you took the coffee bean hopper out and the adjustment knobs come out with it. So if you are trying to line those gear teeth back up correctly, Here is the complete instructions for cleaning the grinder (from wholelattelove.com). You only need the last few steps for lining up the gears.

You do not need to clean the grinder as often as you may think. Usually we do not recommend cleaning the grinder unless there is a problem with calibration or a clog. Avoiding oily beans, flavored beans, and beans stored in the fridge or freezer will typically prevent issues.

If you do experience issues with your grinder, cleaning it is the most common solution. To clean your grinder, follow these directions:

1. Remove the water reservoir, turn off and unplug the machine.
2. Take the cover off of the bean hopper and vacuum out the beans.
3. Remove the 3 Phillips head screws that are in the bean hopper.
4. Lift up the bean hopper and set it aside.
5. Open the machine's service door and remove the drip tray and the brew group.
6. Remove the rubber gasket from the top of the grinder area.
7. The grinder is made up of 2 pieces. The inner piece has 4 tabs that the rubber gasket sits on. The outer piece has teeth in a ring on the exterior covering ½ the circumference.
8. Rotate the outer ring 180 degrees counterclockwise. You should be able to lift off the inner ring. There is a red spot on the outer collar which should now be facing the 9 0'clock position when you are at the front of the machine.
9. Vacuum out all of the beans and ground coffee.
10. If possible, use a small pipe cleaner to get grounds out of the "pathway" going to the front of the machine. It is located on the floor of the grinder at about the 5 0'clock position.
11. Above where the brew group would be located, there is a gray triangular tab attached to a door on a hinge. Pull down on the triangle - coffee grounds may come out.
12. Look above the trap door and you will see the other end of the chute. Vacuum out the chute and clean with a pipe cleaner.

Reinstalling

1. Drop the inner burr onto the grinder with the tab that has the red and blue marks facing the right hand side of the machine at approximately the three-o'clock position.
2. Rotate the outer collar so that the red mark lines up the red/blue marks on the inner burr.
3. Reinstall the rubber gasket that goes over the grinder. The slots in the gasket line up with the four tabs of the outer burr.
4. There is a straight piece located directly to the right of the grinder. This is your dosage control. There is a piece that can slide backwards and forwards on this dosage arm. Push this arm all the way to the back of the machine.
5. Set the knobs in the bean hopper to #0 on the grind setting knob. Set the doser knob all the way to the plus setting. Now place the hopper back into the machine.
Note: You may have to rotate one or both of the knobs, a small amount, to get the bean hopper to set down on its supports.
6. Install the 3 screws.
7. Replace the water reservoir.
8. Fill the bean hopper with a cup of beans.
9. Plug in and turn on the machine.
10. Reinstall the brew group and the drip tray.
11. Once the machine warms up, press the small coffee button. When the grinder comes on set the grind setting to 6.
Note: You may have to press the small coffee button twice or 3 times before the machine will make a cup of espresso.

Rotate the bean hopper counter clockwise until it stops. Lift it off. Remove the outer burr with the 2 wings and clean under the burr. Clean the opening going to the chute for ground coffee(inside where the burr was).
Install the outer burr. Install the bean hopper. Rotate the bean hopper to the French press grind (coarsest) and operate the grinder. This will clean the burrs and the passages. If it starts to clog, repeat the last part to clean the burrs and passage. It must be grinding to go to a finer setting, but you can go to a coarser setting any time. Another thing. Turn the grinder upside down (empty) and rotate the bean hopper back and forth to clean the threads of the adjusting burr..

HI
There are 2 knobs in the bean hopper. Turn the large knob to the largest number. You can turn the knob to a larger number any time but it has to be grinding to turn to a smaller number. Now replace everything and make your coffee. Once you have made your coffee you can turn the knob back to a number that was higher than the one you had it on, but only when the grinder is running.
If that didn't do it. Sounds like you have a blockage in you grind passage. Try removing the brew group. Then inside on the roof of the machine where the brew unit was setting there is a drop chute where the coffee is dropped into the brew unit. From the left side of the drop chute pull down and back, and it will drop coffee. This will clear an opening that relieves pressure on the passage. There is a passage inside the drop chute area that goes to the grinder. Vacuum it out. It will be on the right side of the drop chute.
Once that is cleared go to the bean hopper and follow the first part again.

The grind chamber is blocked, remove the beans and brew unit then clean the grinds chamber, then adjust the grind 2 numbers coarser and try again.

This fixes almost all the "beans will not feed or beans will not grind" problems caused by coffee bean dust packed in the burrs. Oily beans cause this problem more fequently.
a. Pour all the beans out the top.
b. Open the settings up all the way and see what else can be poured out. Use your shop vacuum to **** grounds out the spout and backward out the bean bin.
c. Pour in some instant rice and start grinding. Reduce the grind to a small setting like six and then open the settings all the way again. (The grinder will not start at a low setting with the rice in it. If you let it stop, open the settings to about 16 before trying to restart.)
d. Pour out the rice and vacuum out the ground rice.
e. Adjust the grinder to your favorite setting and try a coffee grind. Grind until most of the rice dust is expelled (any remaining trace of rice dust will not affect the flavor of the coffee).

make sure you use very dry non-oily coffee beans

Sometimes the chamber between the grinder and brewer will clog up. Try: Open the grind all the way up to the highest number. Push the grind button and while grinding move the dose knob (the one with the + - sign toward minus. If it does not kick in and dose try it again. If it does take off then leave it on the high number for 3 coffees. Then while the grinder is turning move the two knobs back to whre they were. If this does not work you can reomve the brew unit and right above where it sits in the machine there is a trap door that you can open. Open it and shove someting like a straw up toward the grinder and you should get a bunch of grounds droppiing down. Then try the above procedure a couple more times. If this does not work you may need to google "Saeco repair" and send it to an authorized repair center.