NEED HELP EGS&DME or actual TRANNY

[shitlips007]

My car is not going into 3rd gear. 1997 328i-sedan-Auto

Diagnosis: Fault is the 1th fault to be detected. Output-speed-sensor signals not sent or too high a level of slip in the gearbox.

On the diagnosis report it indicates this:
1. EGS 8.34
Hardware #: 23
Diagnosis index: 40
Bus index 20

Do I have to buy a new EGS or is this a report reading out codes to the actual problem. Could be a wire? maybe a faulty fuse?

2. DME MS41.1
Program control module:1438067
Basic control module 1437806
Hardware # 11
software #60
diagnosis index:30
Bus index: 21
Siemens
Type approval number 1430251

Question: What part number do I quote when ordering this part? How difficult is it to find this part cheaply? Is this a component that needs REPROGRAMMING ONLY.....or am I doing this trail and error to find problems.

And what is a diagnosis index#???

The STEALER wants $2800 and even the STEALER did not hook it up to a transmission machine, they just got a quote from a Tranny specialist.

So I went to the TRANNY specialist on my own:
They hook up the reader from underneath my steering wheel:

It reads out:
EVAP EMISSION OUTPUT (they told me about a cannister and seals)
3rd Gear problem Ratio: (ripe open the tranny and put in a new clutch)

My question is:

Is this a computer sensor problem EGS & ECM/(DME) wires and fuse?

Or do I listen to the specialist because they say its mechanical problem.

thanks

Any advise would be great