Your problem is right here:
The first possible concern, if you have no engagement at all, no reverse even, is the pump shaft splines, which can strip out inside the torque converter. You get no fluid pressure when it just spins. In a continuing no-engagement situation, disconnecting one of the transmission cooler hoses up front will show little pumping instead of pumping out a gallon a minute.
If you are driving the car, and after it commands a 2-1 downshift when you come to a near stop you have no engagement, and neutral-1 also gets you nothing, it's possible that you have clutch bands on the way out for first gear. Otherwise, a slight chance that one of the accumulators which command the transmission has a fault such as broken spring or are sticking (electrical problems should be indicated with codes).
If you're lucky, it's something like the transmission range sensor, (mounted in the tranny instead of on the gear shifter, and run by a cable), which can be electrically tested. More intrusive but still a tranny pull is the SS1 solenoid, or the 1-2 shift valves.
Factory shop manual pinpoint diagnostic procedures should be completely exhausted before pulling the tranny. Unfortunately, roll this into 99% of tranny shops, you'll get a rebuilt transmission bill.
Watch this beast tear down an AXODE in 12 minutes, broken clutch plate discovered at the 4 minute mark.