old apple software can't be installed on new computer?

I have an old revision B iMac (Mac OS 9) and had lots of Adobe and Macromedia software both on the computer's hard drive and on compatible Zip Disks. I've just got a new iMac; well, second hand given to me (Mac OS X VERSION 10.4.4) and wanted to install all my software onto the new computer.

Unfortunately it's not letting me do this because it says that it does not support the program that created them. I can't even install the zip-disk software on the new computer in order to even open up the zip-disk content (I know zip-disks are on their way out for various reasons, but in the meantime I just wanted to be able to access the disks).

I'm not all that au fait with these things, so was wondering if anyone can suggest anything I could do to access the programs or if it's all a lost cause.

I was always aware that you couldn't install up to date software on a relatively old computer, but didn't know the same applied when it is the other way round.

Thanks for any help. :(
EDIT:

Don, I also have a zip disk with loads of fonts saved on it- I can understand that the other software would still not work regardless, but do you know if I'd be able to install just the fonts onto my new iMac by downloading the latest installation software from iOmega?
 
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