The switch on the dash is just to lock out the rear window switches, they do nothing for the door. It's so that children in the back won't continue to operate their windows without parental control.
Here is the inside of a door latch. In this picture it is unlocked, with the child latch off.
I will describe its operation.
The tab on the upper left is where the door striker hits to release the latch. I have seen where Chinese door handles won't hit this striker contact properly, causing it to come off part way down. This can cause the handle to jam part way and the door will not open because it is bound up but it won't go back to normal either. To remedy this, pry out gently between the door and handle base and try to close the handle (push it towards the door). Put some tape over a thin blade screwdriver or gasket scraper to avoid marring the paint.
This is a front door latch, but the opening mechanism is the same. In fact, a rear door latch can be substituted for a front door latch in a pinch.
If you suspect that is not the problem, we go to step 2. In the upper right of the first photo is the latch lock mechanism. Notice it's in the up position, indicating the latch is unlocked. The picture below is of it in the locked position. It physically moves a barrier in the way of the mechanism so it will not work from either handle.
The lever slides into a plastic socket inside the door itself, which is on a pivot, and this is connected to the door actuator inside the door. Pulling up on the door lock should move the pivot enough so the door latch will work. That this is not happening tells me it may be the problem. If the latch lock mechanism can be reached inside the door (you said the door card was removed), try and move it up and then open the door from the outside.
Now, about the inner door latch and child lock, here is how it works.
The inner door latch is connected by a cable to the lower part of the latch. You can see where the arm is at the bottom and the half circle area where the cable housing goes. The cable itself comes out of the cable housing and is attached to the arm inside the latch that goes straight up. It's just to the right of the lower spring that is wrapped around the mechanism. Attached to the end of the cable is a hook shape that goes around this flat metal bar with a notch in it.
So what happens when you pull on the inner door handle is the cable, which is anchored at the half circle arm, pulls on that flat bar with the notch in it, which then pivots at the spring and releases the door latch.
The child lock comes into play in that it is just a small metal tab on a rivit that gets in the way of that arm moving. So when it's to the inside of the latch (to the front of the car) it's active, and when it's pulled out towards the outside of the latch (the rear of the car), it's inactive.
Here is a good picture of the orientation of the child locks. The on the right has the child lock active and the one on the left has it off.
Here is a photo I took to show what's happening on the inside, you can click on it to zoom in.
The one on the right has the child lock active and the one on the left has it off. You can just make out the little metal tab that gets in the way of the bar, so it won't move.
Here is a single picture with the lock in the on position. It may be a little clearer to see the little tab that prevents the bar from moving.
Now, I have seen worn out door latches that made the door very hard to open, and it took some finesse to get it open. Here are a few pictures. You can see the little spring inside has poked through the plastic housing, which was worn away when the door was misaligned due to the hinges being worn out.
Click on the above picture to enlarge. You can just see the spring end poking out of the latch on the left, the one on the right is a good latch for comparison. If you look closely you can see it on the left latch just below and to the right of the upper bolt mount. These are front door latches, which is why they look a little different, but they operate the same.
Here is a closeup of it, with the latch upside down so you can see it better.
To get the handle off, I had to over extend the inner door handle, which meant removing the inner door handle pull piece and pulling on the cable with some pliers. That may or may not work, so if it doesn't, try this on the outer door handle:
*Push the whole door handle and housing to the rear of the car as far as it will move.
*When there, push in on the rearmost part of the door handle housing itself, and while holding it to the car firmly...
*Try pulling on the door latch itself, all the way out.
I have spare rear door handles and door latch mechanisms if nothing works and you have to destroy something to get it off.
Good luck.
~Disclaimer: I typed this from a hotel room in the NH White Mountains on an iPad mini while the wife was sleeping, which was not an easy thing to do since I had to grab the links to the photos and edited it 22+ times. There may be spelling errors or items that I missed....in which case I also blame it on the beer I had while typing this over the last 1 1/4 hours. If parts of it make no sense I'll correct it tomorrow when we have some down time from hiking due to the storms rolling though, probably in the evening but not too late because I'll undoubtedly be having more spectacular local NH beer. ;-)
So if you have any questions that'll also be the earliest time I'll be able to address them. All photos are on my SmugMug site,
here. Feel free to look at them in more detail or at ones I did not post.