|Regarding when it's USB connected.|
USB devices may not work correctly when they're connected to certain USB ports, e.g. ports in a hub or on the front of a desktop case.
See response 3 in this:
External drives require a lot of power, and they won't work properly in all possible USB ports you can plug them into.
See response 1 in this:
Also - examine the USB ports and the USB plugs - make sure the port doesn't have any metal bent out of shape, such that the plug is loose in the port, make sure the plastic blocking plug that prevents you from plugging in a plug upside down is intact, if applicable, and not loose, in both the plug and the port, and make sure the contact fingers in the port are not bent out of position.
Regarding the eSATA connection - that should work for any eSATA port.
Check your SATA data cable. The connector on each end should "latch" into the socket on the drive and on the mboard, or on the drive controller card - it should not move when you merely brush your hand against it near the socket - if it does, mere vibration can cause a poor connection of it - use another SATA data cable that does "latch", or tape the connector in place.
(There is a slight projection or bump on one side of the outside of the connector that "latches" it into the socket - it's easily broken off or damaged).
Inspect the eSATA ports to make sure nothing's damaged or bent out of shape.