TC and OIL PUMP issues are possible because the torque req'd for reverse wd be much less than moving fwd owing to the big difference in gear ratio.(if the tranny was still on the car, u can prove that by shifting into 1st or the lowest gear ans see if it will indeed move.
Then, internal in the tranny is the issue of bands. just like brake shoes, they wear out over time. sometimes, they are adjustable, and sometimes, they just burn out from heavy use.
Consider also... the valve body. a number of solenoids and ball valves that play and move around to shift the direction of ur tranny oil based on the gear that has been selected for the car to run on.... oil supply to these valves are coursed through a transmission filter... clogging of which results in oil starvation, and resultantly... no operation, partial operation, or faulty operation.
Diagnostics(from basic to complex) include:
1) measurement of oil level;
2) color of oil(darker brown colors indicate burnt bands/clutches
3) smell of oil - burnt oil will smell differently than fresh oil
4) resdue found in oilpans... i.e. metal bits in the oil???
5) oil pressures measured at different RPM's (for advanced tech's)
I don't have a lot to go by from what's been said concerning your plight... read on an see if ur prob is anything like the above, or expound more on ur issue. am sure someone here is always willing to help