Why won't your 1984 Honda shadow shift into gear?

I own a 1983 VT750C, the same bike with 45.5cc's extra. The mechanics are the same.

Sara is right, there might be clutch issues. It's cheap and easy to rebuild the clutch. They take a lot of abuse, so here are some other options.

Very simply open the reservoir for Clutch Fluid. If it seems clear and full, then you're good, if it's dirty bleed the hydraulic clutch line and add new fluid.

If that's not it, simply open the Metal panel next to the shifter and there is some 'Spork' looking shifting mechanisms. These should be facing each other, and linked. The 'Spork' might be over to the left or right and not catching to change gears. If this isn't correctable some new parts are in order. Any parts site will give you very good diagrams.

Also a bleeding of the Slave Cylinder, and if it's not working after you've tried ALL this, then you can go for a Clutch swap. It can save you hours if you first re-lubricate all major parts, (New Gear Oil for the Drivetrain, and new Oil and Filter for the Engine.)

A clutch line adjustment seems in order as well.

As far as the stalling, open or close you idle. It's the dial on the Shifter side, just towards the front of Carburetor and Intake. A little black plastic knob, turn counter-clockwise to open the idle, and clockwise to close it. It's probably that. The Shadows are exceptionally good at running low rpms and without throttle with Dual Sparks per Cylinder, so unless you need new Ignition Coils (A big probably not) I think some new Gas, Fluids Changes, a good cleaning of any exposed electrical parts and an idle adjustment will fix the stall.