Help with 2001 camry problem!!!

[Cooldudehere]

Car Specs:
- 2001 Toyota Camry XLE
- Six cylinder engine
- Automatic Transmission

Problem:

The car ODOMETER will not turn on even when engine is running and the car cannot speed up.

When the weather is HOT summer my car has this problem where the ODOMETER will not turn on or suddenly switches off while driving.
When the ODOMETER is NOT ON the car engine acceleration goes down very badly and it will NOT speed up.
When I try to accelerate it will be VERY SLOW acceleration and the RPM meter nearly touches RED zone.
I had bought the car 3 yrs ago around 60K Miles and now it has 90K miles now.
I have NOT done any major service on the CAR.

This problem used to be once in a while but now it is regularly coming and that too while driving it suddenly drops off.
Is there any issue with TRANSMISSION.
The car runs very smoothly when the ODOMETER is ON and there is NO issue with acceleration also.
Do any of you have a suggestion of something to try? Or is it as bad as I have feared? If the transmission needs to be replaced or rebuilt?

Thanks in advance

[Cooldudehere]

Adding more information..

Both the ODOMETER and SPEEDOMETER are not working..the acceleration falls..when I press the gas pedal the RPM meter goes near the RED zone but acceleration is very less...

The odometer is digital electronic display.

Please let me know if you need more details.