How to connect to an external CD/DVD to install an upgrade

I have a 2GHz mac mini core 2 duo with 2 GB DRAM (2007?) running 10.4.11 and its DVD drive doesn't work anymore.

I want to upgrade to a newer mac mini 2.5 GHz Intel Core i5 with 8 GB of DDR3 Ram (2013?) running 10.8.5.

I can't use migration assistant over ethernet between these two OS's as they are too far apart, but firewire 400 to 800 is supposed to be able to link them.

I understand from several forums and Apple that I could upgrade my old mac mini first to 10.6 (via an external DVD/computer), then use migration assistant from the newer mac mini via ethernet to transfer contents of my old mac mini info to the newer mini.

Since the DVD drive in the old mini isn't working, I tried connecting the new optical drive to the old mini but it doesn't recognize it.

So the optical drive functions well and is connected to the newer mini and the two mini's are connected using firewire 400 to 800 cable.

On the new mini, I opened "preferences", then "sharing" and clicked turned on "DVD or CD sharing".

I tried sleeping and restarting both computers from this setup to see if the old mini would recognize the DVD drive connected to the newer mini

but I can't seem to get it to connect or recognize the DVD drive on the newer mini.

I have a lot of mission critical old data in this old mini. I have created both a "Backup" file and a "Carbon Copy Clone" of my old mac mini

on a back up LaCie drive so I think I'm ready to go. I've never linked two macs together except via an office ethernet network.

Looking forward to some much needed words of wisdom.

Thanks in advance.

KS