In your BIOS, is the SATA (and by extension eSata) setup as IDE or AHCI? If IDE (default in most cases), then the external drive has to be turned on BEFORE the PC is turned on, or it won't be recognized. If you switch that to AHCI, your Windows won't boot unless you also edit your registry (since Windows by default doesn't load the AHCI driver).
AH! An odd one, but it make sense. In its original form, eSATA ports have NO power to supply to an external device; hence, all eSATA external drives MUST have their own power supplies. (This has changed for some units now - there is a new system for eSATA that includes power supplied to the external.) BUT ALL USB ports have a limited amount of power available to their devices, and SOME external HDD's actually can run on that power. So it appears your external case with dual connection routes was able to run the unit entirely on power from the USB port without ever turning on its own internal power supply system, whereas the eSATA route never was designed to do that.