Finicky shifting on a 81 KZ440 LTD chain drive

There were two major issues when I bought this bike. One was it wouldn't turn over and I think I solved that problem, we'll see. The other was that I couldn't shift through all the gears. I could go from neutral to first and back to neutral but I couldn't get it to go any in other gears. I was hoping it was a broken return spring but that appeared to be in great shape. I split the case to have a look inside at the transmission hoping it was a broken fork but everything inside seemed to be in order. The only thing that I could see was that it appeared the fork was "catching" in the groove on the drum when I tried to shift from 1st to second. I can spin everything and keep messing with it and it will eventually go in gear. I'm just wondering if this a common Kawasaki problem or if it will be better when the bike is actually moving. Has anyone else experienced this? Go easy on me, this is my first time venturing into anything like this.

If you were trying to shift it through the gears with the engine off what you experienced is perfectly normal. It has a lockout feature (see the 3 balls in diagram below) that prevents it from upshifting when the bike is not running. Ed

I was curious what purpose those served. Now I know! Thanks for the help!