Since, the simm/zip board is broken I take it you have no fast mem?
If you don't have memory the computer can't work correctly! Put some fast mem in ;zips,dips or simms. Leave the chip mem as is. I would also get some other roms and give them a try. Since, you have some Amiga knowledge and maybe the ability to get another A3000. You could swap some parts ram and roms to see if it works.Maybe, a friend could loan you a computer! :-o