Why can my manual transmission only shift into 1st, 2nd, and 5th? on 2004 Chevrolet Cavalier

transmission grinds in 3rd and 4th gears

Asked by for the 2004 Chevrolet Cavalier
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The linkage may need to be checked/adjusted but i would lean toward bad syncronizers or extremely worn/loose shift fork these are internal parts to the transmission.