Others have given you good advice, but I'll just add my 2 cents.
Warm water soakings every day will do wonders for dehydrated sick lizards. But make sure it is shallow and his head is propped up since he's not moving much so he doesn't drown. The soakings are really good but risky with a very sick lizard because of drowning so watch him closely. Just use water. Gatorade will actually not let as much water go in to the lizard due to osmotic pressure of the salts in the gatorade, and you want this guy to absorb as much water as possible.
I would not give mineral oil yet. If this guy is not really responsive he could very easily aspirate and mineral oil in the lungs kills. Once it's there you can't get it out. Warm water soaks a lot of time is enough by itself to get things moving again if there is an impaction (may not be an actual impaction, just a relative impaction from being dehydrated).
Do not feed too much too often - with something that most likely has not been eating the gut reaction is to fill it with food, but this can actually be dangerous. Too much food if the GI tract isn't moving well is just going to sit and rot and cause more problems. Also you can get refeeding syndrome - basically the sudden influx of food is not what the body is used to so it releases too many ions and gets out of balance and they get really sick from it. Not nauseous, it's a dangerous body wide problem. So start with very small amounts. Like much less than you would normally feed a beardie, which seems counterintuitive I know. But after a few days of that you can increase the amount a little, and keep going like that until you work up to actually fattening him back up so the body can gradually adjust and get back on track. 3ml a day is too much. I would do .25mL 3 times a day (he looks like a subadult, if he's a baby then I'd do even less). In a few days you can increase it to .5ml 3 times a day. Then .75ml, etc. Warm baby food, crickets blended, plus a little bit of calcium would do him good.
Make sure he stays warm but beware that if he's not moving much then he may not be thermoregulating. They can actually just sit there and cook when they're too sick or weak to move around, even at temps not fully at basking level. If you see him just sitting where you put him for more than a few hours then move him to a cooler zone for a few hours. Don't put him directly under the basking point.
Good for you for taking him in! I hope he recovers for you!
