'04Cavalier5spdM/T

hi guys. i got an '04 chevy cavalier, 56,000 miles, and the trans. is acting up. i was driving the car, put it into reverse, let go of the clutch and all i got was a spinning sort of grinding noise. i was finally able to get it into gear and get the car home. on the way, i noticed that all the gears when i pull the stick towards me are having trouble. gears 1, 3, and 5 when i push the stick forward work fine. but 2 didn't engage at all and R barely worked, but 4 did work for some reason. but all gears work when the car is cold. i've been told it's either an adjustment or the synchro in the trans. is gone. and when i pull the stick back, it feels like there isn't enough travel to get to the gear i want. any ideas? thanks for the help.

'04Cavalier5spdM/T

come on, guys. i could really use some help on this. where can i make the adjustment?, if that's what it is?