A common mistake is not having the daughter card inserted correctly, either hanging over the socket by one pin, or in backwards. In this case you will usually just see the powerup garbage on the screen. This garbage is just the random bits that are in the character RAM at powerup, and it indicates the CPU was not able to run.
Another common mistake is for the Z80 CPU to have been inserted incorrectly, either backwards, or possibly with a pin bent that did not insert into the socket properly.
The Zaxxon high score save kit will perform an automatic powerup selftest on powerup. Should the kit detect any failure, the screen will indicate what problem was detected.
If the failure indicates "HIGH SAVE BAD", then most likely that means that one of the socketed chips on the HS daughter card is lose. Check to make sure the 8 pin dip (the smallest chip) on the HS daughter card is fully inserted into its socket.
Zaxxon selftest failure