It looks like I'll have to buy two SATA drives for the two new lab machines. I was hoping to use two of our spare IDE drives, but the new motherboards only have a single IDE channel, which is used for the DVD drive. Due to the IDE specification, IDE cables can't be long enough to connect both DVD and HDD to the single IDE channel (see below). The case forces placement of the HDD and DVD drive such that a standard IDE cable cannot cover the distance between the two connections. A stupid reason to have to buy new drives, but there you go.
I can get an 80GB Seagate SATA drive (p/n: ST380811AS) for $61 each right now, and I've put at least two hours in to trying to make this work, so I'm cutting our losses before "fixing" it becomes more expensive than just replacing it.
For future reference, IDE cables are a maximum 18" long, with no more than 12" from blue connector (which can only go to the board) to grey connector (which always goes to the slave drive, if not using cable select) and no more than 6" from grey to black connector (which always goes to the master drive, when not using cable select).