When you asked about the odometer, do you mean the speedometer? Is it working? If it isn't, there could be an issue with the vehicle speed sensor (VSS). However, the odometer wouldn't cause the issue.
I really feel you need to have the computer scanned for codes. It will identify where the problem is coming from. I will tell you there was a technical service bulletin (TSB) put related to a second to third shift issue. That is why I an interested in knowing if there is a code, specifically a P0756. Take a look through this TSB. Hopefully it will shed some light on what I'm trying to explain.
2003 Saturn LW300 V6-3.0L VIN R
A/T - DTC P0756 Diagnostic Hints
Vehicle A/T - DTC P0756 Diagnostic Hints
A/T - DTC P0756 DIAGNOSTIC HINTS
Bulletin No: 01-07-30-036G
Date: May 12, 2008
Diagnostic Tips for Automatic Transmission DTC P0756, Second, Third, Fourth Gear Start
2008 and Prior Passenger Cars and Light Duty Trucks
2008 and Prior HUMMER H2, H3
2008 and Prior Saab 9-7X
with 4L60-E, 4L65-E or 4L70-E Automatic Transmission (RPOs M30, M32 or M70)
This bulletin is being revised to add the 2008 model year. Please discard Corporate Bulletin Number 01-07-30-036F (Section 07 - Transmission/Transaxle).
Some dealership technicians may have difficulty diagnosing DTC P0756, 2-3 Shift Valve Performance on 4L60-E, 4L65-E or 4L70-E automatic transmissions. As detailed in the Service Manual when the PCM detects a 4-3-3-4 shift pattern DTC P0756 will set. Some customers may also describe a condition of a second third or forth gear start that may have the same causes but has not set this DTC yet. Below are some tips when diagnosing this DTC:
This is a performance code. This means that a mechanical malfunction exists.
This code is not set by electrical issues such as a damaged wiring harness or poor electrical connections. Electrical problems would cause a DTC P0758, P0787 or P0788 to set.
The most likely cause is chips/debris plugging the filtered AFL oil at orifice # 29 on the top of the spacer plate (48). This is a very small hole and is easily plugged by a small amount of debris. It is important to remove the spacer plate and inspect orifice # 29 and the immediate area for the presence of chips/debris. Also, the transmission case passage directly above this orifice and the valve body passage directly below should be inspected and cleaned of any chips/debris.
This code could be set if the 2-3 shift valve (368) were stuck or hung-up in its bore. Inspect the 2-3 shift valve (368) and the 2-3 shuttle valve (369) for free movement or damage and clean the valves the bore and the valve body passages.
This code could be set by a 2-3 shift solenoid (367b) if it were cracked, broken or leaking. Refer to Shift Solenoid Leak Test in the appropriate Service Manual for the leak test procedure. Based on parts return findings a damaged or leaking shift solenoid is the least likely cause of this condition. Simply replacing a shift solenoid will not correct this condition unless the solenoid has been found to be cracked broken or leaking.
It is important to also refer to the appropriate Service Manual or Service Information (SI) for further possible causes of this condition.
Let me know.
Saturday, May 16th, 2020 AT 9:37 PM