Hello and thanks for researching this very important question...I am sorry that no one online earlier felt able to discuss this with you, and that your family is having this difficult and distressing experience.

I am concerned about a few things:

1) He has a concussion of his skull that is causing his lethargy;

2) The roots of his teeth may have been pushed up into his sinuses (and this is causing the bleeding from his eyelids);

3) He has internal injuries that are making it impossible for him to eat and heal.

When youngsters are involved, you have to consider if the expense of a veterinary exam and treatments are worthwhile as a teaching experience vis-a-vis Responsible Pet Care, Emergency Pet Care, etc..

A veterinarian may be able to provide you the following:

1) A general exam to evaluate his brain function, the condition of his front dental roots and overall body condition;

2) A steroid medicine to reduce any brain swelling and general shock condition in the body;

3) An antibiotic to help prevent general infection and specific infection of the broken tooth;

4) Some fluids under his skin to correct dehydration and shock;

5) Some high-calorie supplement to help you nurse him along more effectively.

There are no guarantees at all with such a tiny patient, but again this would be something you would attempt for your son's sake. His symptoms do indicate some serious injuries that may result in his passing...prepare yourself for any eventuality.

Not all medicines and handling techniques are safe for small rodents, so you should look for a veterinarian who is familiar with how to treat this species.
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You can try a very tiny bit of pancake syrup to get him some quick-calories...if he is barely conscious or unresponsive (keeps his eyes tightly closed, curled in a ball), then he will choke on anything put in his mouth. Force-feeding is tricky and can be dangerous.

Evaporated Milk (NOT Condensed Milk) is a good food-replacement if he is able to take in anything and swallow at will. This kind of liquid nutrition is good when the mouth is injured. Alternatively, pet stores carry a milk substitute called KMR that is OK for Gerbils to digest.

Medical evaluation is needed for a Gerbil that cannot relate to the world or take in nutrients.

Let me know if you have other questions or concerns by clicking "Reply".

If he is able to swallow, then you can help with tiny TINY drips with long breaks in between...there may indeed be serious damage to his face and jaws that are preventing him from moving his mouth naturally. The broken tooth is quite painful, and he may be concussed. If his sinues are bruised and filled with blood, then he cannot breath properly...this makes swallowing VERY hard.

You have to go VERY slowly...if he gets a drop in his mouth that is too large to swallow, then he will drown.

I would not "ask" him to swallow more than a single tiny drop of syrup/milk every 30 minutes. Go slow...the goal tonight is to get some calories and nutrients into him that his body can use to heal, if possible. If he can gain some strength, his interest may pick up and you will see how much he can manage as hours pass.