Yes. If the choice of switch makes a substantial difference, then it's a hardware issue, though not necessarily in the switch - it may also be the Terastation.
Without wishing to be seen to cast aspersions, the Buffalo Terastation is built to a budget - around $2.45 in resistors, transistors, and solder. It's entirely possible that the signal-level voltages given off by that thing are not considered acceptable by the new switch, whose standards are stricter, but were OK as far as the old switch was concerned.
Otherwise, it could indeed be the new switch. Unlike a "hub", switches are actually relatively sophisticated bits of kit which understand MAC (hardware) addresses and keep internal tabs on which MAC address is to be found on which switch port. When it notices two of those addresses attempting to talk to each other, a switch sets up a temporary link between the ports in question. It's far from a dumb amplifier, and things can go wrong.
I'd suggest borrowing a 3rd switch. Hell, I'd gladly give you one if you lived closer, just to get rid of some hardware and create space! If the third switch also refuses to acknowledge the existence of your "problem" Terastation, that just about seals it.