The problem is internal to the trans, and there are several possibilities. Does it have all forward gears? Here is the list of probables for No reverse, first chart is for 4L80E trans, and second for 4L60E. This is usually a broken internal part in the trans.. common to these Chevy's
https://www.2carpros.com/articles/automatic-transmission-problems
No Reverse
Checks
Cause
Case (7)
The rear band anchor pin is broken or the pin is not positioned.
Center Support (640)
Leaking at the case, or the support is broken.
Center Support Seal (639)
Leaking
Center Support Bolt (25)
"Â The bolt is loose or broken.
"Â The feed hole is blocked.
Rear Band (657)
Broken, worn, or not anchored
Rear Band Apply Pin (73)
The pin is too short or the pin is binding in the case.
Piston (65)
Binding in the case
Seal (66)
Leaking, damaged, or worn
Gasket (63)
Damaged or displaced
Cover (62)
Damaged
Bolts (61)
Broken, loose, or missing
Checkball
Missing
Fluid Pressure
Too low
Direct Clutch Components
Reaction Plates (618)
The splines are worn.
Friction Plates (611)
The splines or the friction are worn.
Spring Assembly (607)
Jammed
Housing (623)
Cracked
Piston (619)
Leaking
Seal (620, 621, 622)
Leaking
Ball Check
Leaking
No Reverse or Slips in Reverse
No Reverse or Slips in Reverse Checks
Causes
Input Housing Assembly
"Â 3-4 Apply ring stuck in applied position
"Â Forward clutch not releasing
"Â Turbine shaft seals missing, cut or damaged
Manual Valve Link
Disconnected
Valve Body Assembly
"Â 2-3 Shift valve stuck
"Â Manual linkage not adjusted
"Â Spacer plate and gaskets incorrect, mispositioned or damaged
"Â Lo overrun valve stuck
"Â Orificed cup plug restricted, missing or damaged
Reverse Input Clutch Assembly
"Â Clutch plate worn
"Â Reverse input housing and drum assembly cracked at weld
"Â Clutch plate retaining ring out of groove
"Â Return spring assembly retaining ring out of groove
"Â Seals cut or damaged
"Â Restricted apply passage
"Â Porosity in piston
"Â Belleville plate installed incorrectly
"Â Excessive clutch plate travel
"Â Oversized housing
Lo and Reverse Clutch
"Â Clutch plates worn
"Â Porosity in piston
"Â Seals damaged
"Â Return spring assembly retaining ring mispositioned
"Â Restricted apply passage
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Thursday, February 25th, 2010 AT 10:48 PM