I am emulating Kirby 64: The Crystal Shards using Project 64, but every ROM that I have found says "Issues (plugin)" under the status column. When starting the game, the controls work up until the point when I hit start new game, then start works, but everything else just stops working. Any thoughts on this issue?
Kirby 64: The Crystal Shards is listed in Project 64 as "Issues (Plugin)" because, according to the Game FAQ included with the emulator:
Project64 18.104.22.168 beta fixes this issue, but you'll have to be a donor to download the beta. If you don't want to spend $20, then Mupen64 will fix the issue.
As for the controls, Kirby 64 is one of the oddballs that uses the D-Pad instead of the control stick. If you're having trouble with all the other buttons, check out NRage's Input Plugin.