'98 VW Cabrio not shifting. List of codes below but are all related to shift solenoid A-E Should I just replace the solenoid?

Based on the symptoms you described, it is possible that the issue is related to the valve body of the transmission. The valve body is responsible for controlling the flow of hydraulic fluid through the transmission and is made up of various valves and solenoids that regulate pressure and flow.
When the winter drive is engaged, the transmission may be bypassing the valve body and locking into third gear directly, which would explain why it starts in third gear when winter drive is engaged. However, the hard shift from 2nd to 3rd and the inability to shift into 3rd without winter drive suggest a problem with the valve body.
It's also possible that there could be a problem with the transmission control module (TCM) or the wiring and electrical connections between the TCM and the transmission. A diagnostic scan tool can help identify any error codes or other issues related to the TCM.
Given that you have already replaced the 2nd to 3rd shift solenoid without any improvement, it may be best to have the transmission inspected by a professional mechanic or transmission specialist who can perform a more thorough diagnosis and determine the exact cause of the problem. They may also recommend a rebuild or replacement of the transmission if the issue is more serious.

1700 is a generic code for many makes and models referring to a transmission issue.1751 is directed to the shift solenoid valve b. May be able to replace just that solenoid and be ok. Cheaper than a transmission.

code p 0780 refers to gear selection--shift malfunction===causes --wiring --TR( transmission range) sensor--shift solenoids ---transmission mechanical fault
take it to an accredited auto transmission specialist shop for an exact diagnosis of the fault
I seriously doubt that you have a transmission box mechanical fault so get a second opinion if a replacement transmission is suggested

Who told u to replace trans?..first thing should have been done was check wiring and connections at transmission and ECM and between the 2...also need to check the pressure control solenoids B and D...its possible the ECM is acting up especially since P2716 came back twice.

P0705 Transmission Range Sensor Circuit malfunction (PRNDL Input)
P0753 Shift Solenoid A Electrical

make sure ur shifter is in park - otherwise it is a repair issue.

You've got a bad shift solenoid. Removal of the transmission pan is required. Solenoids are cheap and easily replaced. Once they are replaced, and the battery reconnected, this problem will most likely be histoy

try getting the 2-3 shift solenoid from your local auto parts store. that's usually the case when it won't shift into 3rd gear.

DO U HAVE ANY SHIFT SOLENOID FAULT CODES? IF NOT THE SOLENOIDS ARE NOT THE PROBLEM HERE, LET ME KNOW, AUTOZONE AND OTHERS CAN RUN A TEST FOR CODES

check the oil level in the transmission