However, in our case, both HDDs were already set to DMA, so that was a dead end. Then the other solution arose, which is a little more involved. It involves editing the registry, and if you're not completely sure what you're doing here, you may want to ask someone more knowledgeable to help you.
Click Start, go to Run, type in REGEDIT, click OK. Navigate to the following key:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Contro l\Class\
{4D36E96A-E325-11CE-BFC1-08002BE10318} (make sure you match the key exactly, as there may be many similar surrounding it).
Expand this key/folder and you'll notice a number of subkeys, numbered 0000, 0001, 0002, and so on. There may only be a couple, though there could be several. Click on each one and look for the item "DriverDesc" in the right pane, and to the right of that, find the ones that say "Primary IDE Channel" and "Secondary IDE Channel." If it says
anything other than that, you are in the wrong subkey.
Once you identify the Primary IDE Channel key, scroll down in the right pane till you find MasterIdDataCheckSum and/or SlaveIdDataCheckSum. If you know for sure whether the drive you need to fix is set to Master or Slave, delete the appropriate key (MasterIdDataCheckSum for Master, SlaveIdDataCheckSum for Slave). If you don't have any idea, it can't really hurt to delete both. Windows will simply re-identify this information on the next reboot.
We deleted both the MasterIdDataCheckSum and SlaveIdDataCheckSum for the Secondary Channel and the MasterId for the Primary Channel; I suspect the Slave drive had both in this case because, on the old motherboard, each drive had its own IDE port, but the new mobo only had one, so both had to share a cable/port.
After deleting the keys and closing the registry, she rebooted the computer, and has been enjoying her shows online ever since, with nary a skip in about two hours of nonstop playback. She even retested the file transfer during a show to see if it did anything, and playback was still fine.
Seems like I nipped another bug. Maybe now I can get back to work *smirk*.