In the cases I've heard of this happening, it usually turned out to be a loose connection in the sockets.
Usually lifting the board a little bit out of the main socket and pushing it back in does the trick to make a good connection.
Also check that the Z80 is fully seated in the socket, that the Z80 is oriented the right way, that none of the pins on the Z80 are bent or broken and that none of the pins on the botton of the kit are broken. (be careful pulling the kit out of the main PCB socket to make sure none of the pins bend or break.)
If you have an NEC D780C model Z80 chip there is a chance that the chip might be incompatible with the kit. There seems to be something about the NEC chips that is a bit more flaky than other brands of Z80. If you have some other Z80 maybe even swap chips with another PCB you might have on-hand, it might also do the trick. SHARP and Zilog brands are good.
I hope that helps resolve the issue. Let us know how things go
