Just to clarify few things about line-level analog audio:
1) it is usually OK to drive multiple inputs from one source (can connect one CD drive to 2-3 sound cards easily)
2) it is usually NOT OK to connect multiple outputs together (even if one output is not playing anything, it's still NOT OK. Two outputs fighting over each other, this is never OK. Please tell me why people think this is OK?)
3) sound cards with multiple CD-ROM connectors is still just one CD-ROM input with three different connectors
So only feed audio to one CD-ROM connector on sound card, so you can't connect two CD-ROMs to one sound card this way. However, a sound card with multiple CD-ROM connectors could be used to forward the audio from CD-ROM drive to second sound card as well, as the connectors are just wired together.
For the second CD-ROM audio, you must use one of either:
-AUX input (they might have same connector than CD-ROM input)
-LINE input jack on bracket
-switch on front panel or rear panel to select which one will feed audio to CD-ROM input
-mix audio of two drives together with resistors
-use SPDIF for the other drive