I have had the inside door panels off on my 06 Spec Sx... when the door was open...
You might have a better chance if you remove the 4 bolts holding the drivers seat to the floor and move the seat out of the way.. (suggestion...disconnect the battery so you won't trip the air bag light when disconnecting the "yellow" seat connectors and reconnect them BEFORE reconnecting the battery...
Also take apart the passenger door to get an idea of how the door comes apart...It is a mirror image of the drivers door. The biggest problem I see will be the screw that is hidden by the door jamb.. You might have to break this portion of the door as there is no way to get to the Philips screw out as it is buried in the jamb...
The "good" thing is ALL Spec SXs and Spec5s interiors are the same and a replacement panel from another Spec5 will match from 2004.5 through 2006.. The dark gray is standard in the SX/5..
It sound like you have a bad door latch that won't release...Especially if the cables are sound on both ends.
Dave

 

I've managed to somewhat get the panel off. When I reach inside the door and feel where the cables go they disappear into a black plastic box. Is there some way to pop the door open or do I have to get into the box?

 

If you are speaking of the area by the door latch (farthest from the door hinges) that is held in by place by 3 or 4 recessed Philips bolts on the outside jamb area...

Kinda a "catch 22"..
To get to the bolts you have to release the door (open) but you can't open the door to get to the bolts because you can't get to the release...

My suggestion would be to either visit a local bone/salvage yard and remove a donor latch and cable ass'y YOURSELF... to gain knowledge of where the latch release parts are...OR tear down the passenger door to see where the release is...(mirror image)

The door release and lock cables are like what you would find on a 10 speed bike for the brake and shift cables. The center cable/wire moves inside a shroud. You need to find where that center cable is attached and pull the lever to release the door...

My 06 Spec SX had a smashed passenger front door and I got the door off by removing the damaged fender and then removed the 4 hinge bolts... Even though the door was still "latched" I was able to remove it that way..Be careful if you go this route with the flexible rubber wire runs....They do disconnect at the A pillar.. pull the rubber boot free and then pull the wiring harness from the pillar. You WILL find that there is a plug/socket inside the pillar... Also unbolt the door catch arm at the pillar...
You can then tear into the now removed door...
Hope this helps....
Keep us posted on your attempts..
Dave