How can I get into my car that has a completely drained battery?

Drilling the lock won't do much as it turns the release and drilling it can make it lock in tighter. Your better option would be to use something like a small needle to clear the key slot or call a locksmith and have them do it, that way if something is damaged they will have the ability to repair it. The reason I say that is because the rear lock cylinder carries a rather high price tag. It is part number 208 750 0191 B if you want to look for one.

Another option would be to use a jump pack under the hood to provide the power to the electronic release.

I've already tried charging the battery through the hood, and it didn't work, hence why I need to replace my battery. And as I said, no locksmith in the area will touch a Mercedes for any reason. I mentioned drilling because that's what the dealer said they might have to do when I tried asking them about it.

I'll try to find something thin enough to fit in the lock so I can clean it out, but if that doesn't work I'll need to break into my trunk somehow.

Try using something like WD40 or break free to spray in the lock, then see if you can use something like a straightened fish hook to clean out the lock.
What did the car do when you put a charger on it? Was it a modern charger? I ask because many of the newer chargers will not put out any charge if it's truly a dead battery, instead they will shut off the charging section. If you can hook a small jump pack or another battery in parallel they will usually start charging. Or if you can find one of the older chargers that has no fancy circuitry they will usually work as well. I suggest a jump pack because they will normally put out enough power to make things work, even with a drained battery.

I used a Cen-Tech 4-in-1 Portable Power Pack to try and jump my battery through the hood. I'm retrying it now just in case, but it wasn't working when I first tried it. I'm also going to see if I can get someone to try and jump it with their battery.

As for the lock, I don't have a fish hook but I do have a pair of pliers that have sharp tips, and I may have some DW40 somewhere, so I'll try that if jumping doesn't work. The lock has a shield so I can't see inside and it's difficult to get a light inside or take a picture, but whatever is inside feels pretty solid.

The locks are generally set up so the key pushed a small cover out of the way to access the pins, the problem is that if it hasn't been used in a long time or ever, they can fill up with dust, dirt and moisture and freeze up. Put the pack on and turn on the key, if it's sending power the dash should at least come on. If the battery is very discharged it may have frozen, for that the smaller pack might not have enough power to do anything. For that you might see if any of the local garages or road service have a vehicle they send out for these situations. Those are usually set up with large batteries or more than one and can deliver a big jolt to start even frozen batteries. If you are in an area that doesn't get that cold you could get a regular manual battery charger and just leave it on there a while. One that says manual on it like in the image (which is in the same store your jump pack came from). Put it on there at the middle setting and see what the battery does, if it takes a charge then let it charge an hour or so and see what it does then. If it got that low the battery will need to be replaced but that should at least get you in.
I would try to avoid drilling the lock if at all possible, Last I looked the replacement was over $300.00 plus installation and having the keying changed.