2000 xkr with no sport mode symptoms are no light on switch ever and starts out in 2nd gear.
test procedure is as follows: with key (on)
1. check fuse 19 at drivers side fuse box
2. check for power at sport mode switch pin 8 white with red tracer
3. check for power out of sport mode switch at pin 9 red with blue tracer with digital volt meter because this is a resisted circuit.
4. check for power at tcm plug #3 red with blue tracer
This is all the circuit needs to work the rest of the wires are only relevant to the lights and will not effect the function of sport mode.
If you want to skip all this and just get sport mode working permanently or for testing purposes simply install a 1k ohm resister from pin 3 to pin 29 on the tcm and enjoy permanent sport mode and first gear starts for life.