I seem to recall reading that there's a (lame) technical reason that USB cards need to live in the first slot, but it's been years and I might be confusing it with FireWire, SCSI, or any of the dozens of previous generations of "wonder technologies" whose entire purpose in life was to...complicate the serial cable.
If it's not consistent, though, then yeah, the motherboard is probably having issues. To paraphrase a Marvel character, it could be Solderin' Time, in theory, if you have the patience. But more likely, yes, "new computer" time.
(For reference, the Western Digital externals have a screw underneath a case-camouflaged sticker on the side. Pry off the sticker, remove the screw, and the case comes right apart. I point this out because the sticker is pretty close to invisible until you start looking for it specifically and the screw does a shockingly good job of holding the case shut. I thought I was going to lose a finger trying to pull it apart...)