I have a 2000 Z28 with a clutch problem. When I press on the clutch pedal while the vehicle is running, I can't get the tranny to go into any gear. The pedal seems like it has no pressure. I can turn the vehicle off and it will go into all the gears fine. If the car is running and I press on the clutch pedal, you can see the car try to move forward (while in neutral). Has anyone come across this problem or know what is going on here.

 

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This sounds like you are having issues with the hydraulic system in general. The transmission will shift without the engine running regardless of if the clutch is engaged.

Since your slave is inside the bel housing, a Mityvac is likely your best bet to attempt to remove air from the system:
https://ls1tech.com/forums/texas-mem...h-mityvac.html

Also check for any leaks in the system during this process. The master cylinder is directly below the brake booster and is a bit of a pain to get to. The line will run from there down to the transmission down following the firewall.

If clearing air from the system does not resolve the issue, then you have either a bad master or slave cylinder.

Again, since the slave is inside the bel housing, I would personally replace the master cylinder first.