Actually, I'm pretty sure it's not Kickstart incompatibilties, since I own an A600 and have infact played those very games/demos on it without any problems under Kickstart 2.05.
However, I have two ideas what might be the cause:
1) Faulty drive. Since it stops loading halfway, the drive may be kaput/dirty. The drive can be replaced/cleaned, but be sure to find the proper version!
2) Faulty disks. I had that happen sometimes. A game works fine for a long time and suddenly it stops loading... Unfortunately there's not much to do other than replacing the disks and making a backup copy to new floppies/harddisk.
It could also be tons of other stuff, but if the CIA's/Paula (the chip that handles floppydisks) are broken, wouldn't other stuff also malfunction (like the mouse/sound)?
Anyway, maybe my ideas help :-)