A few things I’d like clarified, namely ‘lock knob’ and ‘cord’. Lock knob sounds like the lock cylinder (where the key goes) and that’s clearly how everyone else is interpreting it, however, I’ve never seen one on a back door. Do you mean something on the inside like door handle or whatever the thing is called that the person can manually move to lock or unlock the door? In any case, if my first thought would be to make sure the child safty switch isn’t flipped on. Now, I know that’s only desinged to disengage the door handle on the inside, but I’d still check it. After that, I’d remove the inner door panel and just take a look at all the linkage. I’d me willing to get something fell off or broke.
Upon re-reading this, I see that the door can’t even be opened until you get it unlocked. My first (shade tree mechanic) thought would be to lock and unlock, both with the key and the inside part, rapidly several times to see if you can get something to catch. That in and of itself may be enough to fix the problem. However, if you get it opened that way I’d then try using a screwdriver or something to set the catch and try ‘opening the door’ a few times to see if it made a difference. Also, be prepared to go from whatever step you use to open the door to fixing it all in one day since there’s a chance that once it’s opened, it might not close again.
More thoughts:
You say that pulling the cord (I assume you mean linkage, it’s metal rod, right) doesn’t do anything because it’s locked, have you tried pulling on that while working the lock? Cars have a funny way or working when they’re jiggled, sometimes things jiggle into place for just long enough to work.
You also mentioned that you can’t get the panel off since some of the clips require the door to be open, but if you can get even some of them off, say the ones at the top, along the window, you might be able to hold it back just far enough to get something down there (like a hanger) to release the catch.
There are electronic means that I can think of, if it has electronic locks, but if hear it moving when you hit the unlock button, it’s not going to do anything. If you don’t hear anything, it may be worth exploring that option. Could be easy, could be a PITA, but ultimately, it would just require finding the wires that lock/unlock that that door and applying 12v to them. (But this is assuming the other doors work and/or all fuses and wiring are in good shape).
I agree, it sounds like a linkage issue, personally, after exausting the ‘easy’ options. Ya know, yelling at it, spitting on it, swearing at it, jiggling the moving parts while working the inner and outer door handle and lock, I’d really spend some more time trying to get the panel off, even partially. From there you might be able to at least see what’s going on, if you can see, you can probably get something down there to open the door*, if not, once it’s started, you can probably, carefully, ‘rip’ the rest of the clips out. Sucks to have to do it, but suck is life.
*Again, keep in mind that you should probably make the time between opening the door and fixing it, one day. If you can at least get the top open and see what’s going on, and it looks like you’re going to need parts, I’d strongly suggest getting them (locally, so you can buy all the parts you might need and return what you don’t need) before you jimmy the door open. Once you do get it open, replacing linkage is typically fairly straight forward, even if it includes, handles or catches.
Something to test, if you don’t already know, when the working doors are locked, are the handles free moving (I assume so) like they’re not doing anything or do they ‘stop’ like there’s something blocking them?
Also, make sure to check Google and/or youtube, lots or problems (or at least related problems) are addressed there. Remember to look at similar vintage cars of the same make, so you have a Prism, don’t just stick to Chevy Prism, but Chevy Prism, Geo Prism, Chevy Cavalier and other other compact car from that time frame and, to be honest, most cars work somewhat similar so if someone is showing you how to fix this on their 2003 Tahoe or 2008 Grand Am, it’s probably worth a look.