Speedometer not displaying speed and car won't shift out of first in autoshift and will shift into first and second only with paddle shifters. Reverse can also be selected

VSS - vehicle speed sensor problem maybe . Without test this is just a guess . Having a scanner an checking for DTC'S - diagnostic trouble codes would be the first step in the diagnostic process . Know how the speedometer gets it's info. would be good too.
Speedometer Gauge The hybrid electronic instrument cluster (HEC) (10849) receives the vehicle speed signal from the powertrain control module (PCM) (12A650) over the standard corporate protocol (SCP) network and displays it on the speedometer gauge. If the instrument cluster receives no vehicle speed signal after one second, the speedometer defaults to 0.0 km/h (0.0 mph).

slips in reverse too? (other shoe falls off......)
same answer for all a/t slush boxes.
linkage from shifter to box ok?>
check levels first.
check fuses, if TCM acts dead, (wont autoshift)
change the filter,
get it serviced.
if frisky, read the FSM and do the stall tests and the line pressure tests. otherwise get it fixed.

Check speed sensor at transmission.

There is something not connected, What was the original issue?

may be you need a Odometer Correction Tools

It may be your speed sensor. When the speed sensor is not working, the speedometer will not work, the car will not shift past second gear, and the engine light should appear.

This is the speed in and speed out sensors on the transmission. I just had the same problem. The sensors are about 25 dollars and are easy to replace

these buttons are for you to change gears manually. should be able to slide shifter over into a slot and shift gears up/down by moving shift arm.

I am going to assume it is a 2001 - 2003 S60/V70 with geartronic.

There are several possibilities. One is that the software needs to be upgraded the the Transmissin Control Module. There were some problems with shift flaring and rough shifting.

Second, There are a couple of Technical Journals for hard shifting on those years. It could be the valve body, or a shift spring that has seperated from the base (the shift servo if I remember right) and is causing a hard shift.

Third is that the transmission itself is failing. 2001 was the first year for the 5 speed transmission and hasn't stood up as well as you would think. By 2003 they had worked out all of the bugs and they are once again almost bullet proof (that's of no help to you I know).

If you have a good extended warranty I would take it to a trusted mechanic or the dealer and have them look for said Technical Journals.

I hope this helps.

Check your speed sensor. located on the tranny. AT tranny wont shift if you have a bad speed sensor.